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 6400ft2 and the base of each of the triangles is 70ft, what is the total length of the gutter she’ll need to replace?

The length of the gutter = 2(70) + 80 = 220 ft

Recall:

Thus, the length of the gutter in the image shown below (see attachment) is:

2(base length of triangle) + side length of square

Area of square = 6400 ft² = s²

Side length = s = √6400

s = 80 ft

Base of triangle = 70 ft

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Step-by-step explanation:

If the area of the square is 6400ft², it means that the length of each side of the square is √6400 = 80ft

It means that the opposite side of each triangle is 80ft. Since each triangle is a right angle triangle, we would find the length of the hypotenuse, L by applying Pythagorean theorem which is expressed as

Hypotenuse² = opposite side² + adjacent side²

L² = 80² + 70²

L² = 11300

L = √11300

L = 106.3 ft

The total length of the gutter would be the sum of the sides of the square and the two triangles.

Total length = 106.3 + 106.3 + 70 + 70 + 80 + 80 = 512.6 ft