The ratio of the length of the sides of a rectangle is 5: 2, and its area is 90 square feet. Find the length of the sides.

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hala718 | High School Teacher | (Level 1) Educator Emeritus

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Let L be the length of the rectangle and w be the width.

Then, we know that L > W.

Given the ratio between the length and the width is 5:2

==> L/W = 5/2 

We will cross multiply.

==> 2L = 5W

==> L = (5/2)*W..............(1).

Given that the area of the rectangle is 90.

Then, A = L*W = 90

We will substitute with L = (5/2)*w

==> A = (5/2)*w * w = 90

==> (5/2)*w^2 = 90

Now we will multiply by 2/5.

==> w^2 = 90*2/5 = 36.

==> w= 6.

==> L = (5/2)*6 = 15.

Then, the length of the rectangle is 15, and the width is 6.

To check : L/w = 15/6 = 5/2

Then, the ratio is 5:2

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