The area of a rectangle is 15 square centimeters and the perimeter is 16 square centimeters. What are the dimensions of the rectangle?
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calendarEducator since 2010
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Let the length of the rectangle be L and the width be W.
The perimeter of the rectangle = 2*(L+W) = 16
The area of the rectangle = L*W = 15
L+ W = 8
=> L = 8 - W
Substitute in L*W = 15
=> (8 - W)*W = 15
=> 8W - W^2 = 15
=> W^2 - 8W + 15 = 0
=> W^2 - 5W - 3W + 15 = 0
=> W(W - 5) - 3(W - 5) = 0
=> (W - 3)(W - 5) = 0
W = 3 and W = 5
L = 8 - W = 5 and 3
The required length is 5 and the width is 3.
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calendarEducator since 2008
write3,662 answers
starTop subjects are Math, Science, and Social Sciences
Given that the area of the rectangle is 15 cm^2.
Also, given that the perimeter is 16 cm^2
We need to find the length of the sides.
==> Let the sides be L and w.
==> L*W = 15 ...........(1)
==> 2L + 2W = 16
We will divide by 2.
==> L + W = 8 ..............(2)
We will use the substitution method to solve.
==> L = 8- w
==> (8-W) * W = 15
==> 8W - W^2 = 15
==> W^2 - 8W +15 = 0
==> (w-3)(W-5) = 0
==> W1= 3 ==> L1= 5
==> W2 = 5 ==> L2 = 3
But the length must be greater than the width.
Then, the length is 5 and the width is 3.