Question

max has sticks of lengths 6, 7, 8, and 10 inches. he wants to make a right triangle for an art project. which 3 sticks should he use?
o 6 in., 7 in., and 8 in.
o 6 in., 7 in., and 10 in.
o 6 in., 8 in., and 10 in.
o 7 in., 8 in., and 10 in.

Explanation:

Step1: Recall Pythagorean theorem

For a right - triangle, \(a^{2}+b^{2}=c^{2}\), where \(c\) is the longest side (hypotenuse) and \(a\) and \(b\) are the other two sides.

Step2: Check option 1

For lengths 6, 7, 8: \(6^{2}+7^{2}=36 + 49=85\), \(8^{2}=64\), since \(85
eq64\), it's not a right - triangle.

Step3: Check option 2

For lengths 6, 7, 10: \(6^{2}+7^{2}=36 + 49 = 85\), \(10^{2}=100\), since \(85
eq100\), it's not a right - triangle.

Step4: Check option 3

For lengths 6, 8, 10: \(6^{2}+8^{2}=36+64 = 100\), \(10^{2}=100\), since \(6^{2}+8^{2}=10^{2}\), it is a right - triangle.

Step5: Check option 4

For lengths 7, 8, 10: \(7^{2}+8^{2}=49 + 64=113\), \(10^{2}=100\), since \(113
eq100\), it's not a right - triangle.

Answer:

C. 6 in., 8 in., and 10 in.