Question 762657
The equation for the area of a rectangle is A=L*W
The equation for the perimeter of a rectangle is P=2L+2W
Given: A=1200 & P=150
Equation 1: {{{1200 = L*W)))
Equation 2: {{{150 = 2L + 2W}}}
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Start by solving equation 2 for one of the variables.
Equation 2: {{{150 = 2L + 2W}}}
Subtract 2L from both sides.
{{{150 - 2L = 2W}}}
Factor out a 2 on the left side of the equation.
{{{2*(75-L) = 2W}}}
Divide both sides by 2.
{{{75 - L = W}}}
Now plug (75-L) into equation 1 for W.
Equation 1: {{{1200 = L*W)))
{{{1200 = L*(75 - L)}}}
Multiply the L through.
{{{1200 = 75L - L^2}}}
Subtract 1200 from both sides.
{{{0 = -L^2 + 75L - 1200}}}
Now you can use the quadratic equation to solve for L.
*[invoke quadratic "L", -1,75,-1200]
You will end up with two values for L.
L is equal to 23.14 & 51.86
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Using the values for L, solve for W.
{{{75 - L = W}}}
{{{75 - 23.14 = W}}}
{{{highlight(51.86 = W)}}}
or
{{{75 - 51.86 = W}}}
{{{highlight_green(23.14 = W)}}}
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In other words the length and width can be switched but the dimensions have to be 23.14ft and 51.86ft