Question

A rectangle has a length 2 m less than twice its width. When 5 m are added to the​ width, the resulting figure is a square with an area of 144m2. Find the dimensions of the original rectangle.

Answer 1

Let's start by assigning variables to the dimensions of the rectangle. Let's say that the width is w meters, then the length is 2w - 2 meters (since the length is 2 m less than twice the width).

When 5 meters are added to the width, the resulting figure is a square with an area of 144 square meters. This means that the new width is w + 5 meters, and the new length is also w + 5 meters (since it's a square). We can write an equation for the area of this square:

(w + 5)^2 = 144

Simplifying the equation, we get:

w + 5 = 12

w = 7

Now that we know the width of the original rectangle, we can use the expression we came up with earlier for the length:

length = 2w - 2 = 2(7) - 2 = 12

Therefore, the dimensions of the original rectangle are 7 meters by 12 meters.