Question

a triangle has sides with lengths of 20 miles, 48 miles, and 52 miles. is it a right triangle? yes no

Explanation:

Step1: Recall Pythagorean theorem

For a right triangle, \(a^2 + b^2 = c^2\), where \(c\) is the longest side. Here, \(c = 52\), \(a = 20\), \(b = 48\).

Step2: Calculate \(a^2 + b^2\)

\(20^2 + 48^2 = 400 + 2304 = 2704\)

Step3: Calculate \(c^2\)

\(52^2 = 2704\)

Step4: Compare results

Since \(20^2 + 48^2 = 52^2\), the triangle satisfies the Pythagorean theorem.

Answer:

yes