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| Math Central | Quandaries & Queries |
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Question from irvyn, a student: if you are only given the area and the perimeter how do you find the dimension? |
Irvyn,
You didn't say what the shape is but I expect it is a rectangle. Suppose that the rectangle is $x$ units long and $y$ units wide and that its perimeter is $P$ units and it has an area of $A$ square units. This gives the equations
$2(x + y) = P$
and
$xy = A.$
Solve the first equation for $y,$ substitute into the second equation and solve the resulting quadratic for $x.$
Penny
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