Question

Matt's den is 10 feet longer than it is wide. If the dents area is 231 square feet, what are the dimensions of the room?

Answer 1

Answer:

$21\: \mathrm{feet\: by}\: 11 \: \mathrm{feet}$

Step-by-step explanation:

(Assuming the den is a rectangle)

Let $x$ be the length of the den. Because the length is 10 feet longer than the width, the width of the den can be represented as $x-10$.

The area of a rectangle is given as $l\cdot w$, therefore we can form the following equation:

$x(x-10)=231$

Expanding this, we have:

$x^2-10x=231, \\\\x^2-10x-231=0$

This factors into $(x-21)(x+11)=0$, therefore $x=21, \: -11$.

Because -11 is extraneous, the length of the den is $21$ feet and the width is $21-10=11$. Thus, the dimensions of the den are $\fbox{ 21\: \mathrm{feet\: by}\: 11 \: \mathrm{feet} }$.