Question 63560
<b>.the area of a square bookcase is 21 more than the perimeter. find the length of a side</b>

Let L = the side of the bookcase.
Let P = the perimeter of the bookcase.
Let A = the area of the bookcase.

Then, we know that:
{{{A=P+21}}}
{{{A=L^2}}}
{{{P=4L}}}

So, {{{A=L^2=P+21}}}.
But, P=4L so {{{A=L^2=4L+21}}}.
So, {{{L^2 = 4L+21}}}.
Or, {{{L^2-4L-21=0}}}.
This factors to {{{(L+3)(L-7)=0}}}.
So, {{{L=-3}}} or {{{L=7}}}.

The length can't be negative so {{{L=7}}}.

Let's verify the answer.

If {{{L=7}}} then {{{P=4*7=28}}} and {{{A=L^2=7^2=49}}}.
So, A is indeed 21 more than P.