Question

what is the length of the three sides of the right triangle shown? 20,95,980; 10,26,56; 10,24,28; 10,24,26

Explanation:

To determine the sides of a right triangle, we use the Pythagorean theorem \(a^2 + b^2 = c^2\), where \(c\) is the hypotenuse (longest side) and \(a, b\) are the legs. We check each option:

Step 1: Check Option 1 (20, 95, 98)

Calculate \(20^2 + 95^2 = 400 + 9025 = 9425\), and \(98^2 = 9604\). Since \(9425
eq9604\), this is not a right triangle.

Step 2: Check Option 2 (10, 25, 36)

Calculate \(10^2 + 25^2 = 100 + 625 = 725\), and \(36^2 = 1296\). Since \(725
eq1296\), this is not a right triangle.

Step 3: Check Option 3 (10, 24, 26)

Calculate \(10^2 + 24^2 = 100 + 576 = 676\), and \(26^2 = 676\). Since \(10^2 + 24^2 = 26^2\), this satisfies the Pythagorean theorem.

Step 4: Check Option 4 (10, 24, 25)

Calculate \(10^2 + 24^2 = 100 + 576 = 676\), and \(25^2 = 625\). Since \(676
eq625\), this is not a right triangle.

Answer:

C. 10, 24, 26