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?

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