Question

37 ft.
a
35 ft.
what is the perimeter? if necessary, round to the nearest tenth.
feet

Explanation:

Step1: Find the length of side \( a \)

This is a right triangle, so we use the Pythagorean theorem \( c^2 = a^2 + b^2 \), where \( c = 37 \) ft (hypotenuse) and \( b = 35 \) ft (one leg). Rearranging for \( a \): \( a = \sqrt{c^2 - b^2} \).
Substitute values: \( a = \sqrt{37^2 - 35^2} = \sqrt{(37 - 35)(37 + 35)} = \sqrt{2 \times 72} = \sqrt{144} = 12 \) ft.

Step2: Calculate the perimeter

Perimeter of a triangle is the sum of all sides: \( P = 35 + 12 + 37 \).
Add the values: \( 35 + 12 = 47 \), \( 47 + 37 = 84 \) ft.

Answer:

84