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.
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
no this is 7th grade math.
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.
Right Triangle 40^2= 1600 24^2+32^=1600
1600=1600
Can someone give the whole test please?
thank you sooo much.
Your explanation is correct and clear. It effectively explains the concept of the triangle inequality theorem and how it applies to the given lengths of 24, 32, and 40. You provide the calculations and reasoning to show that the third side length of 40 falls within the acceptable range, satisfying the inequality. Overall, your explanation is good.
Thank you
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.