Question 243737
We know the area of a rectangle is width times the length.
{{{A = W * L}}}
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We are told A = 80
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We also are told L is 2 feet longer than the width.
{{{L = W + 2}}}
or
{{{W = L - 2}}}
You pick.
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Substituting what we know:
{{{A = W * L}}}
{{{80 = (L-2) * L}}}
Multiplying through the right-hand:
{{{80 = L^2 - 2L}}}
Equal things are equal, so we can rewrite:
{{{L^2 - 2L = 80}}}
Subracting 80 from both sides
{{{L^2 - 2L - 80 = 0}}}
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We now consider whether it can be factored.  The factors of 80 are 2*40, 4*20, 5*18, 8*10...
We have to have different signs to get them to multiply to -80.
And we need them to be 2 apart to have the solve the L term.  8 & 10 is the way to go.
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{{{(L-10)(L+8) = 0}}}
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So we have two candidate solutions:  L=10 and L=-8.
Since we are talking about the area of a rectangle, a length of -8 is not reasonable.  So we'll test 10.
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Looking back at the equations we established:
{{{W = L - 2 = 10 - 2 = 8}}}
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So we propose the L=10 and W=8.
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Checking the Area, we test:
{{{A = L * W = 10 * 8 = 80}}}
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That checks. So we're done.