Find
Length and Width of a Rectangle
if its
Area and Perimeter
is given
QUESTION: A postcard has an area of 24 square inches. Its perimeter is 20 inches. What are the dimensions of the postcard inches by inches?
SOLUTION:
Let L is the length of the postcard
And W is the width of the postcard
Then
Area of a postcard = L × W = 24 in² ———————(1)
Perimeter of a postcard = 2L + 2W = 20 in ————————-(2)
From Equation (1)
`L = frac{24}{W}` ————————(3)
Put value of L from equation (3) in equation (2)
2L + 2W = 20
`2left(frac{24}Wright)` + 2W = 20
`frac{24}W` + W = 10
24 + W² = 10W
W² – 10W + 24 = 0
W² – 6W – 4W + 24 = 0
W( W – 6) -4(W – 6) = 0
(W – 4) (W – 6) = 0
Thus either
W – 4 = 0 which implies W = 4
Or
W – 6 = 0 which implies W = 6
If W = 4
Put this value of W in equation (3)
`L=frac{24}W=frac{24}4=6` in
If W = 6
Put this value of W in equation (3)
`L=frac{24}W=frac{24}6=4` in
Thus if a postcard has an area of 24 square inches and perimeter of 20 inches, the dimensions of the postcard will be 6 inches by 4 inches.
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