Question

question
which of the following sets of numbers could not represent the three sides of a right triangle?
answer
○ {36, 48, 60}
○ {45, 60, 74}
○ {57, 76, 95}
○ {14, 48, 50}
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Explanation:

Step1: Recall Pythagorean theorem

For right triangle: $a^2 + b^2 = c^2$, where $c$ is the largest side.

Step2: Test set {36,48,60}

$36^2 + 48^2 = 1296 + 2304 = 3600$, $60^2 = 3600$. Valid right triangle.

Step3: Test set {45,60,74}

$45^2 + 60^2 = 2025 + 3600 = 5625$, $74^2 = 5476$. $5625
eq 5476$.

Step4: Verify remaining sets (optional check)

For {57,76,95}: $57^2+76^2=3249+5776=9025$, $95^2=9025$. Valid.
For {14,48,50}: $14^2+48^2=196+2304=2500$, $50^2=2500$. Valid.

Answer:

{45, 60, 74}