Question

which side lengths form a right triangle?
choose all answers that apply:

a 11,13,√290
b 7,24,25
c 2,5,7

Explanation:

Step1: Apply Pythagorean theorem for option A

Check if \(11^{2}+13^{2}=(\sqrt{290})^{2}\).
\(11^{2} = 121\), \(13^{2}=169\), \((\sqrt{290})^{2}=290\).
\(121 + 169=290\).

Step2: Apply Pythagorean theorem for option B

Check if \(7^{2}+24^{2}=25^{2}\).
\(7^{2}=49\), \(24^{2}=576\), \(25^{2}=625\).
\(49+576 = 625\).

Step3: Apply Pythagorean theorem for option C

Check if \(2^{2}+5^{2}=7^{2}\).
\(2^{2}=4\), \(5^{2}=25\), \(7^{2}=49\).
\(4 + 25=29
eq49\).

Answer:

A. \(11,13,\sqrt{290}\), B. \(7,24,25\)