Question 931564
The equation for the area of a rectangle is: A = LxW
Equation 1: {{{L = W + 180}}}
Equation 2: {{{L * W = A}}}
Equation 3: {{{(L+90)*(W-60) = A}}}
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Note that the areas of both rectangles are the same so we can set them equal to each other.
{{{L*W = (L+90)*(W-60)}}}
From equation 1, we now that L = W + 180.
Plug (W + 180) into the equation for L
{{{(W+180)*W = ((W+180)+90)*(W-60)}}}
Simplify
{{{W^2 + 180W = (W + 270)*(W-60)}}}
We can use FOIL on the right side of the equation.
*[invoke foil "(W+270)(W-60)"]
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Rewrite the equation
{{{W^2 + 180W = W^2 + 210W - 16200}}}
Subtract {{{W^2}}} from both sides.
{{{180W = 210W - 16200}}}
Subtract 180W from both sides.
{{{0 = 30W - 16200}}}
Add 16200 to both sides.
{{{16200 = 30W}}}
Divide both sides by 30
{{{highlight(540cm = W)}}}
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Now plug 540 into equation 1 for W
Equation 1: {{{L = W + 180}}}
{{{L = (540) + 180}}}
{{{highlight_green(L = 720cm)}}}