Question

1. the legs of a right triangle are congruent and each have a measure of 8 yards. what is the length, in yards, of the hypotenuse? round your answer to the nearest yard.

Explanation:

Step1: Apply Pythagorean theorem

For a right - triangle, \(a^{2}+b^{2}=c^{2}\), where \(a\) and \(b\) are the legs and \(c\) is the hypotenuse. Given \(a = b=8\) yards.

Step2: Substitute values into the formula

\(c^{2}=8^{2}+8^{2}\). Calculate \(8^{2}=64\), so \(c^{2}=64 + 64=128\).

Step3: Solve for \(c\)

\(c=\sqrt{128}\). Simplify \(\sqrt{128}=\sqrt{64\times2}=8\sqrt{2}\approx8\times1.414 = 11.312\).

Answer:

\(11\) yards