Question

which set of side lengths does not form a right triangle? 36, 77, 85; 16, 63, 65; 38, 80, 90; 14, 15, 29

Explanation:

Step1: Check 36, 77, 85

$$36^{2}+77^{2}=1296 + 5929=7225$$
$$85^{2}=7225$$
Since \(36^{2}+77^{2}=85^{2}\), this is a right - triangle.

Step2: Check 16, 63, 65

$$16^{2}+63^{2}=256+3969 = 4225$$
$$65^{2}=4225$$
Since \(16^{2}+63^{2}=65^{2}\), this is a right - triangle.

Step3: Check 38, 80, 90

$$38^{2}+80^{2}=1444+6400=7844$$
$$90^{2}=8100$$
Since \(38^{2}+80^{2}
eq90^{2}\), this is not a right - triangle.

Step4: Check 14, 15, 29

$$14^{2}+15^{2}=196 + 225=421$$
$$29^{2}=841$$
Since \(14^{2}+15^{2}
eq29^{2}\), this is not a right - triangle.

Answer:

C. 38, 80, 90 and D. 14, 15, 29