Question 121887
The perimeter of a rectangle is given by {{{P=2L + 2W}}}, but we are given that the dimensions of this rectangle always have the relationship {{{L=5W}}}, so let's use that information to express the perimeter in terms of just W:


{{{P=2(5W)+2W}}}
{{{P=10W+2W}}}
{{{P=12W}}}


But now we can express the width, W, in terms of P by dividing by 12:


{{{W=P/12}}}


The area of a rectangle is given by {{{A=LW}}}, but we still know that {{{L=5W}}}, so the area of this rectangle is {{{A=5W*W}}} or {{{A=5W^2}}}


But we have developed an expression for W in terms of the perimeter, P, so let's substitute that for W in the area equation:


{{{A=5(P/12)^2}}}, or


{{{A=5P^2/144}}}