Question 902943
Let L = length of the sign
Let W = width of the sign
Since you are given two unknowns, you will need two equations.
Area(A) of a rectangle = Length x Width
Equation 1: {{{A = L * W}}} (Equation for the area of a rectangle)
Equation 2: {{{L = W + 2}}} (The length of the sign is 2yds more than the width)
Given: A = 34 yds^2
Plug 34 into equation 1 for A
Equation 1: {{{A = L * W}}}
{{{34 = L * W}}}
Notice that equation 2 is already solved for L
Plug (W + 2) into equation 1 for L
{{{34 = (W + 2) * W}}}
Multiply the W through on the right hand side
{{{34 = W^2 + 2W}}}
Subtract 34 from both sides
{{{0 = W^2 + 2W - 34}}}
Now you can use the quadratic equation to solve for W
*[invoke quadratic "W", 1,2,-34]
The quadratic equation tells us that W = 4.916 & -6.916
Since we can not have a negative distance we will only use W = 4.916
Now plug 4.916 into equation 2 for W
Equation 2: {{{L = W + 2}}}
{{{L = (4.916) + 2}}}
{{{highlight(L = 6.916)}}}
The Length of the lawn is 6.196 yards and the Width is 4.916 yards