Friday Riddle - EARLY

nudgie
nudgie Member Posts: 1,478 Member
edited March 2014 in Colorectal Cancer #1
Which triangle has a bigger area: 1. A triangle with sides measuring 300, 400, and 500. 2. A triangle with sides measuring 300, 400, and 700.

Comments

  • msccolon
    msccolon Member Posts: 1,917 Member
    #2
    which triangle
    They would both have the same area as the extra length would just extend past the other two sides, wouldn't it?
    Mary
  • Madre
    Madre Member Posts: 123
    #3
    I agree with Mary. The
    I agree with Mary. The corner angle would change so the height factor would change, so they have the same area.
    Where do you find these? They are great!
  • krystiesq
    krystiesq Member Posts: 240 Member
    #4
    Madre said:

    I agree with Mary. The
    I agree with Mary. The corner angle would change so the height factor would change, so they have the same area.
    Where do you find these? They are great!

    I don't think you can have a
    I don't think you can have a triangle with sides that the sum of two do not equal a larger amount than the third. I think the second triangle, 300, 400, 700 can't exist.
  • PGLGreg
    PGLGreg Member Posts: 731
    #5
    krystiesq said:

    I don't think you can have a
    I don't think you can have a triangle with sides that the sum of two do not equal a larger amount than the third. I think the second triangle, 300, 400, 700 can't exist.

    Area of a line.
    Good point. The second "triangle" would be identical with a 700 unit line which, I guess, has 0 area. The first triangle is a right triangle, and two of them fitted together along their longest side would make a 300 by 400 rectangle, so the area is half of 300 times 400.
    -Greg
  • msccolon
    msccolon Member Posts: 1,917 Member
    #6
    krystiesq said:

    I don't think you can have a
    I don't think you can have a triangle with sides that the sum of two do not equal a larger amount than the third. I think the second triangle, 300, 400, 700 can't exist.

    300,400,700
    that's kind of what i was getting at with the extending beyond thing... to keep it a triangle, the side measure 700 would have to be bisected at some point before the end of the 700 or else the 300 and 400 would have to be back to back to line up end to end, which would make them a single line, not a triangle. Or has chemo just completely fried my math?
    Mary
  • Jimbob-
    Jimbob- Member Posts: 46
    #7
    msccolon said:

    300,400,700
    that's kind of what i was getting at with the extending beyond thing... to keep it a triangle, the side measure 700 would have to be bisected at some point before the end of the 700 or else the 300 and 400 would have to be back to back to line up end to end, which would make them a single line, not a triangle. Or has chemo just completely fried my math?
    Mary

    If memory serves me
    If memory serves me correctly the Formula for the area of a triangle is 1/2 The Sum of the legs. Therefore they would be the same......
  • 4law
    4law Member Posts: 110
    #8
    not a fair question :-)
    Show me a 300, 400, 700 triangle and I'll give you an answer.
  • PGLGreg
    PGLGreg Member Posts: 731
    #9
    Jimbob- said:

    If memory serves me
    If memory serves me correctly the Formula for the area of a triangle is 1/2 The Sum of the legs. Therefore they would be the same......

    Almost ...
    The area of a right triangle is 1/2 the product of the legs.
    -Greg
  • StacyGleaso
    StacyGleaso Member Posts: 1,233 Member
    #10
    TRIED to resist...
    I tried to resist, but couldn't........

    To begin with, let's review the pythagorean theorem..."a" squared plus "b" squared equals "c" squared. Using that equation, 300 squared plus 400 squared DOES equal 500 squared. So that triangle IS legitimately able to be drawn. The second triangle, however, does NOT fall into that category, meaning, the triangle is unable to be drawn as a RIGHT triangle. 300 squared plus 400 squared will NEVER equal 700 squared. Take it a step further, though, and realize that the pythagorean theorem only applies to RIGHT triangles. So the second triangle CAN exist, but it will NOT be a right triangle, but instead an obtuse triangle. To give you a visual of what it would resemble, think of a metal clothes hanger and pushing the center apex part down closer to the bottom straight part. The "700" triangle is VERY "slim".

    Secondly, the area of a triangle is determined by one half base times height. So if you determine the "500" triangle to have an area of 60,000 (getting this figure by multiplying 300 by 400 and dividing by two). The area of the "700" triangle is not so easily determined since it is NOT a right triangle, and you must figure out what the height is. Using rough numbers, the area of the "700" triangle is 48,412.

    THEREFORE....I think the triangle with dimensions of 300, 400, and 700 has a smaller area than the one with the dimensions of 300, 400, and 500.

    Although, I could be wrong, too! lol

    Hugs,

    Stacy
  • 4law
    4law Member Posts: 110
    #11
    krystiesq said:

    I don't think you can have a
    I don't think you can have a triangle with sides that the sum of two do not equal a larger amount than the third. I think the second triangle, 300, 400, 700 can't exist.

    I don't think you can have a
    unless I'm missing something, you are correct -- that's why I asked to see a 3,4,7 triangle
  • PGLGreg
    PGLGreg Member Posts: 731
    #12
    StacyGleaso said:

    TRIED to resist...
    I tried to resist, but couldn't........

    To begin with, let's review the pythagorean theorem..."a" squared plus "b" squared equals "c" squared. Using that equation, 300 squared plus 400 squared DOES equal 500 squared. So that triangle IS legitimately able to be drawn. The second triangle, however, does NOT fall into that category, meaning, the triangle is unable to be drawn as a RIGHT triangle. 300 squared plus 400 squared will NEVER equal 700 squared. Take it a step further, though, and realize that the pythagorean theorem only applies to RIGHT triangles. So the second triangle CAN exist, but it will NOT be a right triangle, but instead an obtuse triangle. To give you a visual of what it would resemble, think of a metal clothes hanger and pushing the center apex part down closer to the bottom straight part. The "700" triangle is VERY "slim".

    Secondly, the area of a triangle is determined by one half base times height. So if you determine the "500" triangle to have an area of 60,000 (getting this figure by multiplying 300 by 400 and dividing by two). The area of the "700" triangle is not so easily determined since it is NOT a right triangle, and you must figure out what the height is. Using rough numbers, the area of the "700" triangle is 48,412.

    THEREFORE....I think the triangle with dimensions of 300, 400, and 700 has a smaller area than the one with the dimensions of 300, 400, and 500.

    Although, I could be wrong, too! lol

    Hugs,

    Stacy

    How slim?
    'So the second triangle CAN exist, but it will NOT be a right triangle, but instead an obtuse triangle. To give you a visual of what it would resemble, think of a metal clothes hanger and pushing the center apex part down closer to the bottom straight part. The "700" triangle is VERY "slim".'

    Right. If the longest side were 500, then, as you say, the angle between the two other sides, on either side of the hook of the clothes hangar, would be 90 degrees. As the longest side increases, the angle between the 300 and 400 length sides increases from 90 degrees, and the area of the triangle gets smaller and smaller. How large can the angle get? (Answer: 180 degrees.) How small can the area become? (Answer: 0.)
  • Jimbob-
    Jimbob- Member Posts: 46
    #13
    PGLGreg said:

    How slim?
    'So the second triangle CAN exist, but it will NOT be a right triangle, but instead an obtuse triangle. To give you a visual of what it would resemble, think of a metal clothes hanger and pushing the center apex part down closer to the bottom straight part. The "700" triangle is VERY "slim".'

    Right. If the longest side were 500, then, as you say, the angle between the two other sides, on either side of the hook of the clothes hangar, would be 90 degrees. As the longest side increases, the angle between the 300 and 400 length sides increases from 90 degrees, and the area of the triangle gets smaller and smaller. How large can the angle get? (Answer: 180 degrees.) How small can the area become? (Answer: 0.)

    So we actually end up with a
    So we actually end up with a Straight Line.Zero area
  • vinny3
    vinny3 Member Posts: 928 Member
    #14
    Heron's formula
    I think that because the second triangle has one longer side it lowers the height of the triangle and thus there is less area. Found a formula on the internet for determining the area of a triangle and it would indicate that the 300,400, 500 triangle has a bigger area than the 300,400,700 one.

    ****
  • StacyGleaso
    StacyGleaso Member Posts: 1,233 Member
    #15
    PGLGreg said:

    How slim?
    'So the second triangle CAN exist, but it will NOT be a right triangle, but instead an obtuse triangle. To give you a visual of what it would resemble, think of a metal clothes hanger and pushing the center apex part down closer to the bottom straight part. The "700" triangle is VERY "slim".'

    Right. If the longest side were 500, then, as you say, the angle between the two other sides, on either side of the hook of the clothes hangar, would be 90 degrees. As the longest side increases, the angle between the 300 and 400 length sides increases from 90 degrees, and the area of the triangle gets smaller and smaller. How large can the angle get? (Answer: 180 degrees.) How small can the area become? (Answer: 0.)

    Bottom Line
    So the bottom line is that the "500" triangle has a greater area than the "700" triangle.

    Wow...this "Early Friday" puzzle is running right up to Friday! lol

    Happy Thursday,

    Stacy
  • Kanort
    Kanort Member Posts: 1,272 Member
    #16
    Oh My!
    I can't tell you how my "right" brain is spinning right now. Tee Hee!!

    Hugs,

    Kay
  • vinny3
    vinny3 Member Posts: 928 Member
    #17
    vinny3 said:

    Heron's formula
    I think that because the second triangle has one longer side it lowers the height of the triangle and thus there is less area. Found a formula on the internet for determining the area of a triangle and it would indicate that the 300,400, 500 triangle has a bigger area than the 300,400,700 one.

    ****

    Jimbob has it
    Once I went to bed I remembered a principle of math from years ago. If you multiply something by zero the answer is zero. The second triangle has no area so it is a straight line. I guess if you put 300 and 400 together it comes out to 700 so no formula was really needed but it has been fun.

    ****
  • kimby
    kimby Member Posts: 797
    #18
    HUH???
    I claim chemo brain this week. Besides, I always hated geometry -- too many rules....I never could follow all the rules in life....
  • CherylHutch
    CherylHutch Member Posts: 1,375 Member
    #19
    kimby said:

    HUH???
    I claim chemo brain this week. Besides, I always hated geometry -- too many rules....I never could follow all the rules in life....

    HUH 2!!
    Hahaha... I'm with you, Kimby!! Geometry/Math... never my strong point. Now, after reading everyone's explanations and formulas on how to come to the answer, my brain is so muddled, I think I've forgotten what a triangle looks like!! Hahahaha!

    Cheryl
    Math'less in Vancouver

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