Math CentralQuandaries & Queries


Question from irvyn, a student:

if you are only given the area and the perimeter how do you find the dimension?


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

$2(x + y) = P$


$xy = A.$

Solve the first equation for $y,$ substitute into the second equation and solve the resulting quadratic for $x.$


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