SOLUTION: A rectangle sign must have an area of 34 square yards. Its length must be 2 yards more than its width. Find the exact dimensions of the sign.

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Question 902943: A rectangle sign must have an area of 34 square yards. Its length must be 2 yards more than its width. Find the exact dimensions of the sign.
Answer by Stitch(470)   (Show Source): You can put this solution on YOUR website!
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: (Equation for the area of a rectangle)
Equation 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:

Notice that equation 2 is already solved for L
Plug (W + 2) into equation 1 for L

Multiply the W through on the right hand side

Subtract 34 from both sides

Now you can use the quadratic equation to solve for W
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation (in our case ) has the following solutons:



For these solutions to exist, the discriminant should not be a negative number.

First, we need to compute the discriminant : .

Discriminant d=140 is greater than zero. That means that there are two solutions: .




Quadratic expression can be factored:

Again, the answer is: 4.91607978309962, -6.91607978309962. Here's your graph:

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:


The Length of the lawn is 6.196 yards and the Width is 4.916 yards
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