The length of a rectangle is 4 cm more than the width. What are the dimensions if the area is 165 cm2 .

Answer 1

The area of a rectangle is length (l) * width (w), so lw=165

Given that we know that the length is 4 cm more than the width, we can say that l = w+4 and substitute that into our equation.

Our equation becomes (w + 4) * w = 165 which we can simplify to w² + 4w = 165

We can solve by completing the square. What is the closest perfect square to 165? 169 (13 squared). To get from 165 to 169, i have to add 4, so I have to add 4 to the other side of the equation to keep it balanced.

w² + 4w + 4 = 169

Factor that:

(w + 2)² = 169

w + 2 = ±√169

w + 2 = ± 13

In this real-world situation, we can ignore the negative root because we can have a negative side length.

So w + 2 = 13

Subtract 2 from each side and w = 11.

So the width is 11. Since the length is 4 more than the width, the length is 11+4, or 15 cm.

Answer 2

L = 4 + W

Area = 165 = LW = 4W + W²

By quadratic formula W = 11 (and there is an extraneous root

L=15, W=11, A=165

Answer 3

Assign variables: L = length. W = width

2 unknowns require 2 equations:

You are given:

L = W + 4

Area = L*W = 165

Use the 1st equation to replace L in the second:

(W + 4) * W = 165

W² + 4W = 165

Solve by completing the square:

W² + 4W + 4 = 165 + 4

(W + 2)² = 169

W + 2 = ±13 (ignore the negative root)

W = 11

Use either one of the original equations to get L = 15