The perimeter of a rectangle is 15.2 km, and it's area is 11.88 km^2. Find it's length and width

The perimeter of a rectangle is 15.2 km, and its area is 11.88 km^2. Find its length and width.

Length ≈ 5.4 km

With ≈ 2.2 km

Explanation:

Let P be the perimeter of a rectangle and A its area. Let W and L be, respectively, the width and length of the rectangle. Find W and L in terms of P and A.

solution:

P = 2 * W + 2 * L (1)

and

A = W * L (2)

solve equation (1) for W:

W = P / 2 - L

and W by P / 2 - L in A = W * L to obtain

A = L * (P / 2 - L)

Rewrite as a standard quadratic equation in L

L^ 2 - L (P / 2) + A = 0

Solve the above equation for L and find W using W = P / 2 - L.