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.

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