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 hypotenuse (the longest side) and \(a\) and \(b\) are the legs.

Step2: Test each set of side - lengths

• For the set \(6\) in., \(7\) in., \(8\) in.: \(6^{2}+7^{2}=36 + 49=85\), \(8^{2}=64\), since \(85

eq64\), it's not a right - triangle.

• For the set \(6\) in., \(7\) in., \(10\) in.: \(6^{2}+7^{2}=36 + 49 = 85\), \(10^{2}=100\), since \(85

eq100\), it's not a right - triangle.

• For the set \(6\) in., \(8\) in., \(10\) in.: \(6^{2}+8^{2}=36+64 = 100\), \(10^{2}=100\), so \(6^{2}+8^{2}=10^{2}\), it is a right - triangle.
• For the set \(7\) in., \(8\) in., \(10\) in.: \(7^{2}+8^{2}=49 + 64=113\), \(10^{2}=100\), since \(113

eq100\), it's not a right - triangle.

Answer:

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