# DimensionsCalculateĀ the dimensions of rectangle if the perimeter is equal to area

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Student Comments

giorgiana1976 | Student

Area of the rectangle is the product of the length and the width.

A = l*w

On the other hand, the perimeter of the rectangle is:

P = 2(l+w)

According to enunciation, we'll put the area and the perimeter in the relation of equality:

l*w = 2(l+w)

Now, we'll form the second degree equation, when knowing the product and the sum of the length and width.

x^2 - Sx + P = 0

We'll use Viete's relations:

l + w = S

l*w = P

But, l*w = 2(l+w)

P = 2S

x^2 - Sx + 2S = 0

delta = S^2 - 8S

S^2 - 8S = 0

S(S-8) = 0

S = 0 impossible

S = 8

l+w = 8 => l = 8-w

l*w = 16

(8-w)*w - 16 = 0

w^2 - 8w + 16 = 0

w1 = [8+sqrt(64-64)]/2

width = 4 units

length = 4 units

The dimensions of the rectangle have to be equal for the area and the perimeter to be equal.