SOLUTION: A square concrete patio in located the center of the a rectangular yard. The yard is (x + 10) long and (x +8) wide. The concrete patio is (x + 4) long and (x + 4) wide. The area o
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-> SOLUTION: A square concrete patio in located the center of the a rectangular yard. The yard is (x + 10) long and (x +8) wide. The concrete patio is (x + 4) long and (x + 4) wide. The area o
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Question 1084126: A square concrete patio in located the center of the a rectangular yard. The yard is (x + 10) long and (x +8) wide. The concrete patio is (x + 4) long and (x + 4) wide. The area of just the grass is 264 ft^2 Answer by Theo(13342) (Show Source):
the area of just the grassy part of the yard is 264 square feet.
if you take the area of the grassy yard and subtract the area of the concrete patio, you will have the area of just the grassy part of the grassy yard.
what you get is (x+10) * (x+8) - (x+4)^2
simplify this to get:
x^2 + 8x + 10x + 80 - (x^2 + 8x + 16)
simplify this a little further to get:
x^2 + 8x + 10x + 80 - x^2 - 8x - 16
combine like terms to get:
10x + 64
this is the area of the grassy part of the grassy yard that is equal to 264 square feet.
you get:
10x + 64 = 264
subtract 64 from both sides of this equation to get:
10x = 200
solve for x to get x = 20
the area of the grassy yard is (x+10) * (x+8)
when x = 20, this becomes 30 * 28 = 840 square feet
the area of the concrete patio is (x+4)^2.
when x = 20, this becomes 24^2 = 576 square feet.
subtract the area of the concrete patio from the area of the grassy yard and you get 840 - 576 = 264 square yards.
