A triangle has side lengths of 10", 24", and 26". Is the triangle a right triangle? Justify your Response.

The triangle with side lengths 10", 24", and 26" is a right angle triangle

Explanation:

Given:

Sides of a triangle:

a = 10 in

b = 24 in

c = 26 in

To prove: right angle triangle

Using pythagoras theorm:

(c) ² = (a) ² + (b) ²

(26) ² = (10) ² + (24) ²

676 = 100 + 576

676 = 676

Right hand side is equal to left hand side.

Thus, the triangle with side lengths 10", 24", and 26" is a right angle triangle