Question 327379
The formula for perimeter of a rectangle is,
{{{P=2*L+2*W=42}}}
1.{{{L+W=21}}}
The formula for area of a rectangle is,
{{{A=L*W=104}}}
2.{{{L*W=104}}}
From eq. 1,
{{{L=21-W}}}
Substitute into eq. 2,
{{{(21-W)W=104}}}
{{{21W-W^2=104}}]
{{{W^2-21W+104=0}}}
You can factor this quadratic,
{{{(W-13)(W-8)=0}}}
Two solutions:
{{{W-13=0}}}
{{{W=13}}} Then from above,
{{{L+13=21}}}
{{{L=8}}}
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{{{W-8=0}}}
{{{W=8}}}
{{{L=13}}}
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The rectangle is 13 miles by 8 miles.