# 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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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.**

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.**