SOLUTION: The length of a rectangle is five less than twice the width. The area is 42 square yards. Find the dimensions of the rectangle

Question 146769:
The length of a rectangle is five less than twice the width. The area is 42 square yards. Find the dimensions of the rectangle
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
Let x=width and y=length

Since "The length of a rectangle is five less than twice the width", this means that . Also, because "The area is 42 square yards", this tells us that the area equation is which becomes

Start with the second equation

Plug in

Distribute

Get all terms to the left side.

Combine like terms.

Notice we have a quadratic equation in the form of where , , and

Let's use the quadratic formula to solve for x

Start with the quadratic formula

Plug in , , and

Square to get .

Multiply to get

Rewrite as

Add to to get

Multiply and to get .

Take the square root of to get .

or Break up the expression.

or Combine like terms.

or Simplify.

So the widths are or

However, since a negative width is not possible, this means that the only answer for the width is

Go back to the first equation

Plug in

Simplify

So the width is 6 yards and the length is 7 lards
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