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Question 926725: The area of a rectangle is four times the area of a square. If the rectangle is 36 inches long, and the width of the rectangle is the same as the length of a side of the square, find the dimensions of both the rectangle and the square.
Find in inches:
The length of rectangle
The width if rectangle
Side length of square
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! the area of the rectangle is equal to L*W
the are of the square is equal to S^2
L = length of rectangle
W = width of rectangle
S = side of square
you are given that L = 36
you are given that W = S
you are given that the area of the rectangle is equal to 4 times the ares of the square.
this means that:
L*W = 4*S^2
since W = S, replace W in this equation with S to get:
L*S = 4*S^2
divide both sides of this equation by S to get:
L = 4*S
since L = 36, this equation becomes:
36 = 4*S
solve for S in this equation to get:
S = 9
since S = W, this means that W = 9 as well.
area of the rectangle = L*W = 36 * 9 = 324 square inches.
area of the square is equal to 9^2 = 81 square inches.
multiply 81 * 4 and you get 324 square inches which is the area of the rectangle.
the area of the rectangle is equal to 4 times the area of the square as it should be.
your solution is:
length of the rectangle is 36 inches.
width of the rectangle is 9 inches.
length of the side of the square is 9 inches.
area of the rectangle is 324 square inches.
area of the square is 81 square inches.
the length of the rectangle was given and not really solved for.
the rest of the measurements were solved for.
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