Question

The wards decided to use carpet tiles in the family room. The room has an area of 176 square feet and is 5 feet longer than it is wide. Find the dimensions of the family room

Answer 1

The dimensions of the room are length is 16 feet and the width is 11 feet.

Explanation:

Given:

The wards decided to use carpet tiles in the family room. The room has an area of 176 square feet and is 5 feet longer than it is wide.

Now, to get the dimensions.

Let the width be
`x.`

So, the length =
`x+5.`

Area = 176 square foot.

So, we put formula of area to get the dimensions:

Area = length × width.

`176=(x+5)* x`

`176=x^2+5x`

Subtracting boths sides by 176 we get:

`0=x^2+5x-176\\x^2+5x-176=0`

On solving the equation:

`x^2+16x-11x-176=0\\x(x+16)-11(x+16)=0\\(x+16)(x-11)=0`

As,

`x+16` = 0

`x=-16`

So, we would not take the negative result.

Thus,

`x-11=0\\x=11`

So, the width = 11 feet.

Now, to get the length by substituting the value of
`x`:

`x+5\\=11+5\\=16`

The length = 16 feet.

Therefore, the dimensions of the room are length is 16 feet and the width is 11 feet.