Question

The length of a rectangle is four times its width.

If the perimeter of the rectangle is 100 ft, find its area.

Answer 1

The answer is 400 ft^2.

Step-by-step explanation:

Preliminaries: Know that for a rectangle-

Length(L) x Width(W) = Area(A)

2 x (L+W) = Perimeter(P)

Step-by-step explanation:

Since length is 4 times width, we will represent length as 4W and width as W.

L=4X

W=X

P=100ft

Since we know that perimeter is 2 x (L+W) = P, we simply need to sunstitute in our values above and we get 2 x (4X + X) = 100

Solving further we get

2 x (5X) = 100

10X = 100

X = 10

We can solve for Length now, substituting in 10 for X. The equation 4X then becomes 4 x 10 which is 40

We now know that our width is 10 ft long and our length is 40 ft long. Using the equation Length(L) x Width(W) = Area(A), we get 40ft x 10ft = A

We finally get A = 400ft^2