Question

margaret needs to put a new gutter on one side of her roof. the shape of her roof is made up of two right triangles that are on each side of a square. if the area of the square is 4900 ft² and the base of each of the triangles is 75 ft, what is the total length of the gutter shell need to replace?

Explanation:

Step1: Find the side length of the square

The area formula of a square is \(A = s^{2}\), where \(A\) is the area and \(s\) is the side - length. Given \(A = 4900\space ft^{2}\), then \(s=\sqrt{4900}\).
Since \(\sqrt{4900}=\sqrt{70\times70}\), so \(s = 70\space ft\).

Step2: Calculate the total length of the gutter

The total length of the gutter is the sum of the side - length of the square and the bases of the two right - triangles.
The formula for the total length \(L\) is \(L=s + 75+75\).
Substitute \(s = 70\) into the formula: \(L=70 + 75+75\).
First, \(75+75=150\), then \(L=70 + 150\).

Answer:

\(220\)