Question

determine which set of numbers shown forms a right triangle. a {20, 48, 52} b {25, 60, 65} c {15, 36, 39} d all of the above

Explanation:

Step1: Recall Pythagorean theorem

For a right - triangle with side lengths \(a\), \(b\), and hypotenuse \(c\), \(a^{2}+b^{2}=c^{2}\).

Step2: Check option A

Let \(a = 20\), \(b = 48\), \(c = 52\). Then \(a^{2}=20^{2}=400\), \(b^{2}=48^{2}=2304\), \(c^{2}=52^{2}=2704\). And \(a^{2}+b^{2}=400 + 2304=2704=c^{2}\).

Step3: Check option B

Let \(a = 25\), \(b = 60\), \(c = 65\). Then \(a^{2}=25^{2}=625\), \(b^{2}=60^{2}=3600\), \(c^{2}=65^{2}=4225\). And \(a^{2}+b^{2}=625+3600 = 4225=c^{2}\).

Step4: Check option C

Let \(a = 15\), \(b = 36\), \(c = 39\). Then \(a^{2}=15^{2}=225\), \(b^{2}=36^{2}=1296\), \(c^{2}=39^{2}=1521\). And \(a^{2}+b^{2}=225 + 1296=1521=c^{2}\).

Answer:

D. All of the above