Question

determine which sets of lengths can form a right triangle. right triangle yes no 11, 60, 61 14, 90, 95 7, 24, 25 submit

Explanation:

Step1: Apply Pythagorean theorem for \(11,60,61\)

Check if \(11^{2}+60^{2}=61^{2}\).
\(11^{2} = 121\), \(60^{2}=3600\), \(121 + 3600=3721\).
\(61^{2}=3721\). So \(11^{2}+60^{2}=61^{2}\).

Step2: Apply Pythagorean theorem for \(14,90,95\)

Check if \(14^{2}+90^{2}=95^{2}\).
\(14^{2}=196\), \(90^{2} = 8100\), \(196+8100 = 8296\).
\(95^{2}=9025\). Since \(8296
eq9025\).

Step3: Apply Pythagorean theorem for \(7,24,25\)

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

Answer:

For \(11,60,61\): Yes.
For \(14,90,95\): No.
For \(7,24,25\): Yes.