Question 903448
Let L = the length of the rectangle
Let W = the Width of the rectangle
The equation for the Area of a rectangle is A = L x W
The equation for the perimeter of a rectangle is P = 2L + 2W
-----------------------
Equation 1: {{{144 = L * W}}}
Equation 2: {{{L = 4W}}} (The rectangle is 4 times as long as it is wide)
Equation 3: {{{P = 2L + 2W}}}
Note that equation 2 is already solved for L.
Plug (4W) into equation 1 for L
Equation 1: {{{144 = L * W}}}
{{{144 = (4W) * W}}}
Combine like terms
{{{144 = 4W^2}}}
Divide both sides by 4
{{{36 = W^2}}}
Take the square root of both sides
{{{sqrt(36) = sqrt(W^2)}}}
{{{highlight(6 = W)}}}
-----------------------
Now plug 6 into equation 2 for W
Equation 2: {{{L = 4W}}}
{{{L = 4*(6)}}}
{{{highlight_green(L = 24)}}}
-----------------------
Now Plug L=24, and W=6 into equation 3
Equation 3: {{{P = 2L + 2W}}}
{{{P = 2*(24) + 2*(6)}}}
Simplify
{{{P = 48 + 12}}}
{{{highlight(P = 60)}}}
The perimeter is 60ft