Question 9674
You could try this:

A = L X W = 90 m^2  This is the area.

P = 2(L+W) = 38 m  This is the perimeter. Solve this for L and substitute in the above equation, then solve for W.

2(L+W) = 38
L+W = 19
L = 19-W

{{{(19-W)W = 90}}} Simplify and solve for W
{{{19W - W^2 = 90}}}
{{{W^2 - 19W + 90 = 0}}} Solve this quadratic by factoring.
{{{(W-9)(W-10)= 0}}} Apply the zero product principle.

W-9 = 0 or W-10 = 0

If W-9 = 0, then w = 9
If W-10 = 0, then W = 10

These two numbers are actually the length and the width of the rectangle.

L = 10 m and W = 9 m.

Check:
A = LW = 10(9) = 90 m^2
P = 2(L+W) = 2(10+9) = 2(19) = 38 meters.