Question

using the side lengths of the given triangles (not drawn to scale), determine which ones are right triangles.

Explanation:

Step1: Recall Pythagorean theorem

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

Step2: Test green triangle (15,36,39)

Longest side $c=39$. Calculate $15^2 + 36^2 = 225 + 1296 = 1521$, $39^2 = 1521$.

Step3: Test blue triangle (18,25,30)

Longest side $c=30$. Calculate $18^2 + 25^2 = 324 + 625 = 949$, $30^2 = 900$. $949
eq 900$.

Step4: Test purple triangle (8,15,18)

Longest side $c=18$. Calculate $8^2 + 15^2 = 64 + 225 = 289$, $18^2 = 324$. $289
eq 324$.

Step5: Test yellow triangle (9,38,42)

Longest side $c=42$. Calculate $9^2 + 38^2 = 81 + 1444 = 1525$, $42^2 = 1764$. $1525
eq 1764$.

Step6: Test pink triangle (7,24,25)

Longest side $c=25$. Calculate $7^2 + 24^2 = 49 + 576 = 625$, $25^2 = 625$.

Step7: Test brown triangle (13,?,35)

Incomplete side length, cannot verify.

Answer:

The right triangles are:

1. The triangle with side lengths 15, 36, 39
2. The triangle with side lengths 7, 24, 25

The triangle with incomplete side lengths (13, ?, 35) cannot be verified, and the other triangles are not right triangles.