Question

Question #9000b

Answer 1

`l=19` units
`w=9` units

Explanation:

The area of a rectangle is given by the formula `A=lw`. We are given the area to be `171` units and that the width is 10 units less than the length. We can express this as `l-10` or letting `w=l-10`. Visually, the problem looks like this:

We can therefore come up with the following equation to find the dimensions:

`l*(l-10)=171`

Where `l` is the length and `l-10` is the width and `171` is the area

We solve for `l`

`l^2-10l=171`

Notice how this has become a factoring problem.

`l^2-10l-171=0`

To factor, we must find two numbers whose product is `-171` and sum is `-10`. These numbers are `9` and `-19`.

`(l+9)(l-19)=0`

We set this as two separate equations and solve for `l`

`l+9=0 , l-19=0`

`l=-9,l=19`

We can ignore the `-9` because we can't have a negative dimension. Therefore the length is `19` units.

Thus, to find the width recall that we expressed the width as `w=1-10`.

`:. w= 19-10=9`.

The width is `9` units.

So the dimensions are `19` by `9` units