Question

a triangle has sides with lengths of 39 inches, 80 inches, and 89 inches. is it a right triangle? yes no

Explanation:

Step1: Recall Pythagorean theorem

For a right triangle, the sum of the squares of the two shorter sides should equal the square of the longest side. The formula is \(a^2 + b^2 = c^2\), where \(c\) is the longest side.

Step2: Identify sides

Let \(a = 39\), \(b = 80\), \(c = 89\).

Step3: Calculate \(a^2 + b^2\)

\(39^2 = 1521\), \(80^2 = 6400\), so \(a^2 + b^2 = 1521 + 6400 = 7921\).

Step4: Calculate \(c^2\)

\(89^2 = 7921\).

Step5: Compare

Since \(a^2 + b^2 = c^2\) (7921 = 7921), the triangle satisfies the Pythagorean theorem.

Answer:

yes