Question

1. which measurements could not represent the side lengths of a right triangle?10.5, 14, 17.515, 36, 394, 7.5, 9$9\frac{3}{5}$, 18, $20\frac{2}{5}$clear all

Explanation:

Step1: Recall Pythagorean theorem

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

Step2: Test Option 1: 10.5,14,17.5

Calculate $10.5^2 + 14^2 = 110.25 + 196 = 306.25$; $17.5^2 = 306.25$. Equal, so right triangle.

Step3: Test Option 2: 15,36,39

Calculate $15^2 + 36^2 = 225 + 1296 = 1521$; $39^2 = 1521$. Equal, so right triangle.

Step4: Test Option 3: 4,7.5,9

Calculate $4^2 + 7.5^2 = 16 + 56.25 = 72.25$; $9^2 = 81$. $72.25
eq 81$, not right triangle.

Step5: Verify Option4 (optional): $9\frac{3}{5},18,20\frac{2}{5}$

Convert to decimals: 9.6,18,20.4. Calculate $9.6^2 + 18^2 = 92.16 + 324 = 416.16$; $20.4^2 = 416.16$. Equal, so right triangle.

Answer:

C. 4, 7.5, 9