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Math, Ms. Sue Help asap plss

Can the numbers 24, 32, and 40 be the lengths of three sides of a triangle? Why or why not

My answer: Yes it can. Because the 3 lengths satisfy the triangle inequality theorem. The triangle inequality theorem states that the third side of a triangle must be greater than the positive difference of the given two sides and must be less than the sum of the given two sides. For example, given 24 and 32.The third side, x > (32 - 24), x >8 and x < (24 + 32), x < 56. Therefore, 8 < x < 56. So x must be greater than 8 and less than 56.So the third side, x, is between 8 and 56. The third side can not be 8 and it can not be 56, but must fall in between 8 and 56.And the third side 40 satisfies the inequality 8 < x < 56.40 falls between 8 and 56.Therefore 24, 32 and 40 can be the three sides of a triangle.
Is this good or not? pls tell me so i can make it better.

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  1. An easy way to think of it:
    the sum of any two must be greater than the third.

    So , yes, they form a triangle.
    You are correct.

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  2. you can also do a quick check and note that
    24, 32, and 40 are just 8 times 3,4,5 -- a well-known right triangle

    or, using the longest and shortest sides, check that the third side must obey

    40-24 < 32 < 40+24
    it works

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  3. Is this 6th grade math?

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  4. no this is 7th grade math.

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  5. The answer:

    Yes it can. Because the 3 lengths satisfy the triangle inequality theorem. The triangle inequality theorem states that the third side of a triangle must be greater than the positive difference of the given two sides and must be less than the sum of the given two sides. For example, given 24 and 32.The third side, x > (32 - 24), x >8 and x < (24 + 32), x < 56. Therefore, 8 < x < 56. So x must be greater than 8 and less than 56.So the third side, x, is between 8 and 56. The third side can not be 8 and it can not be 56, but must fall in between 8 and 56.And the third side 40 satisfies the inequality 8 < x < 56.40 falls between 8 and 56.Therefore 24, 32 and 40 can be the three sides of a triangle.
    Is this good or not? pls tell me so i can make it better.

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  6. Thank you

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  7. thank you sooo much.

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  8. Right Triangle 40^2= 1600 24^2+32^=1600
    1600=1600

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