Question

which side lengths form a right triangle?
choose all answers that apply:
a 2, 2, \sqrt{4}
b 9, 40, 41
c \sqrt{5}, 10, \sqrt{125}

Explanation:

Step1: Check option A

For side lengths \(2\), \(2\), \(\sqrt{4} = 2\).
Since \(2^{2}+2^{2}=4 + 4=8\) and \(2^{2}=4\), \(2^{2}+2^{2}
eq2^{2}\).

Step2: Check option B

For side lengths \(9\), \(40\), \(41\).
Calculate \(9^{2}+40^{2}=81 + 1600=1681\) and \(41^{2}=1681\). So \(9^{2}+40^{2}=41^{2}\).

Step3: Check option C

For side lengths \(\sqrt{5}\), \(10\), \(\sqrt{125}=5\sqrt{5}\).
Calculate \((\sqrt{5})^{2}+10^{2}=5 + 100 = 105\) and \((5\sqrt{5})^{2}=125\), \((\sqrt{5})^{2}+10^{2}
eq(5\sqrt{5})^{2}\).

Answer:

B. \(9,40,41\)