Question 600385
let the rectangle's length = L and rectangle's width = W

{{{L*W = 60, so L = 60/W}}}


{{{L^2 + W^2 = 13^2}}}
{{{(60/W)^2 + W^2 = 169}}}
{{{3600/W^2 + W^2 = 169}}}
multiply all by {{{W^2}}}
{{{3600 + W^4 = 169W^2}}}
{{{W^4 - 169W^2 + 3600 = 0}}}
Factorize it into:
{{{(W^2 - 144)*(W^2 - 25) = 0}}}
{{{W^2 - 144 = 0 or W^2 - 25 = 0}}}
{{{W^2 = 144}}} or {{{W^2 = 25}}}
{{{W=12}}} or {{{W=-12}}} or {{{W =5}}} or {{{W=-5}}}
because the dimension of a rectangle can't be negative numbers, so
W = 12 or W = 5
if W = 12 then L = 60/12 = 5
if W = 5 then L = 60/5 = 12


so the dimension of the rectangle is 12 ft x 5 ft