Question

applying the converse of the pythagorean theorem
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?
○ 6 in., 7 in., and 8 in.
○ 6 in., 7 in., and 10 in.
○ 6 in., 8 in., and 10 in.
○ 7 in., 8 in., and 10 in.

Explanation:

Step1: Recall converse Pythagorean rule

For sides $a,b,c$ ($c$ longest), $a^2 + b^2 = c^2$ for right triangle.

Step2: Test 6,7,8

$6^2 + 7^2 = 36 + 49 = 85$; $8^2 = 64$. $85
eq 64$

Step3: Test 6,7,10

$6^2 + 7^2 = 85$; $10^2 = 100$. $85
eq 100$

Step4: Test 6,8,10

$6^2 + 8^2 = 36 + 64 = 100$; $10^2 = 100$. $100 = 100$

Step5: Verify 7,8,10 (optional)

$7^2 + 8^2 = 49 + 64 = 113$; $10^2 = 100$. $113
eq 100$

Answer:

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