Answer:
l = 28 ft; w = 20 ft
Step-by-step explanation:
We have two bits of information
(a) The perimeter of the rectangle
The formula for the perimeter of a rectangle is
P = 2l + 2w
P = 96 ft Insert into the formula
(1) 2l + 2w = 96
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(b) The length-to-width ratio
l/w = 7/5 Multiply both sides by w
(2) l =(7w)/5
Substitute the value of l from Equation (2) into Equation (1)
2×(7w)/5 + 2w = 96
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Solve for w
(14w)/5 + 2w = 96 Multiply each side by 5
14w + 10w = 480 Combine like terms
24w = 480 Divide each side by 24
w = 20 ft
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Solve for l
Substitute the value for w into Equation (1).
2l +2×20 = 96
2l +40 = 96 Subtract 40 from each side
2l = 56 Divide each side by 2
l = 28 ft
The rectangle is 28 ft long and 20 ft wide.
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Check:
P = 2×28 + 2×20
P = 56 + 40
P = 96 ft
Also
l/w = 28/20
l/w = 7/5
