the length of a rectangel is 8 inches more than its width. the area of the rectangel is 128 square inches.find the dimentions of the rectangle
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the length of a rectangel is 8 inches more than its width. the area of the rectangel is 128 square inches.find the dimentions of
Answer:
The length of the rectangle is equal to 16 INCHES and the width of the rectangle is equal to 8 INCHES.
Step-by-step explanation:
Let L and W be the length and width of the rectangle, respectively
L = W + 8
From the equation, we can state that W = L - 8
AREA = 128 sq in
The formula of an area of a rectangle is length times its width
A = LW
FIND THE VALUE OF W
1. Substitute the derived value of L (L=8+W) to the equation of the area (A=LW)
A = (W + 8) * W
128 = (W + 8) * W
128 = W^2 + 8W
2. Add 16 to the both sides of the equation so that the right side will form a perfect square binomial
128 + 16 = W^2 + 8W + 16
144 = (W + 4)^2
3. Square both sides of the equation
12 = W + 4
W = 12 - 4
W = 8 in ANS
FIND THE VALUE OF L
1. Substitute the value of W to the equation of L
L = W + 8
L = 8 + 8
L = 16 in ANS
CHECKING:
AREA = LW
128 sq in = 16 in * 8 in
128 sq in = 128 sq in