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.
