# The length of a rectangle is 5 yd less than double the width, and the area of the rectangle is 52 yd^2 . How do you find the dimensions of the rectangle?

##### 2 Answers

Width = 6.5 yds, length = 8 yds.

#### Explanation:

Define the variables first.

We could use two different variables, but we have been told how the length and width are related.

Let the width be

The length =

"Area = l x w" and the area is given to be 52 squ yards.

To factorise, find factors of 2 and 52 which cross-multiply and subtract to give 5.

We have the correct factors, now fill in the signs. We need -5.

Each factor could be equal to 0

The width = 6.5 yards. Now find the length: 6.5 x 2 -5 = 8 yards

Check:

Width = 6.5yds, length = 8yds

Area = 6.5 x 8 = 52

Length

Width

#### Explanation:

Let width be

Therefore, length

We know that

Inserting given and assumed numbers we get

rearranging we obtain

To factorize we use split the middle term method. We have two parts of middle term as

Paring and taking out common factors we have

Setting each factor equal to

Check:

Area