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

Answer:

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

Step-by-step 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.

$176=(x+5)\times x$

$176=x^2+5x$

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.