How do you find the length and width of a rectangle when the perimeter and area are given?

it cannot be solved

------------------------------------------------

Actually, you can. Suppose, as an example, that the rectangle's area and perimeter are 6 and 10 respectively. Let therectangles length and width be represented by L and W respectively. Then

LW = 6 (a) and

2 ( L + W ) = 10 (b)

Let me rearrange (b) to obtain an expression for W: W = 5 - L.

Now let me substitute this expression for W in (a): L ( 5 - L ) = 6.

This is a quadratic equation that one can solve for L. Let me do it by factoring,

L^2 - 5 L + 6 = 0 = ( L - 2 ) ( L - 3 )

This implies that L=2 or L=3. With L=2, W=3; with L=3, W=2. Put simply the rectangle's length and width are 3 and 2 respectively.