Question

the diagram below is a right triangle formed by 3 squares. select 3 side lengths that can form this triangle. 8 12 16 20 25

Explanation:

Step1: Recall Pythagorean theorem

For a right triangle, \(a^2 + b^2 = c^2\), where \(a\), \(b\) are legs and \(c\) is hypotenuse.

Step2: Test combinations

• Check \(12^2 + 16^2 = 144 + 256 = 400 = 20^2\).
• Other combinations: \(8^2 + 12^2 = 64 + 144 = 208

eq 16^2(256)\), \(8^2 + 16^2 = 64 + 256 = 320
eq 20^2(400)\), \(12^2 + 20^2 = 144 + 400 = 544
eq 25^2(625)\), etc.

Answer:

12, 16, 20 (corresponding to the side lengths that satisfy \(12^2 + 16^2 = 20^2\) for the right triangle formed by the squares, using the Pythagorean theorem).