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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?

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Answer:

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

akposevictor

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

Recall:

  • Area of a square = [tex]s^2[/tex]; where, s is the length of a side (all its side are equal.)

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

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

Learn more here:

https://brainly.com/question/813881

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