Question

A rectangle’s width is 2 meters shorter than its length, l. Its area is 168 square meters. Which equation can be used to find the length of the rectangle?

Answer 1

L² + 2L - 168 = 0 is the equation that can be used to get the length of the rectangle.

Explanation:

Let the length of the rectangle is L and width is W.

Now rectangle's length is 2 meters shorter than its length.

So the equation will be

L = W - 2------(1)

Area of the rectangle is 168 meters²

A = Length × Width

168 = L× W

168 = L× (L + 2) [ From equation 1]

168 = L² + 2L

L² + 2L - 168 = 0

Therefore, L² + 2L - 168 = 0 is the equation that can be used to find the length of the rectangle.

Answer 2

Depends on answer choice given.

`l^2-2l-168\\or\\169=(l+1)^2\\or\\ l=12, w=10`

Explanation:

To find the area of a rectangle, use the formula A=l*w. Here the area is 168, the length is l and the w=l-2.

`A=l*w\\168= l*(l-2)\\168=l^2-2l\\0=l^2-2l-168`

This is the area formula. It can be manipulated and solved by completing the square as shown below:

`168+1=l^2-2l +1\\169 = (l+1)^2\\13=(l+1)\\12=l`

This means the width is w = 12-2 = 10

The length is 12 and the width is 10.