We are making a rectangular table with an area of
10 square feet. The dimensions of a rectangle are its length and width. Recall that the is length times width.
A=ℓw⇒10=ℓw
We know that the
length of the table is one foot shorter than twice its width. Let's call the
width of the table
x. The length can be written as
ℓ=2x−1.
10=ℓw⇒10=(2x−1)x
We now have an equation with one variable. If we can solve for the width
x, then we can find the length. Let's start by rewriting our equation in .
Let's now factor the left-hand side of the above equation.
2x2−x−10=0
2x2+4x−5x−10=0
2x(x+2)−5x−10=0
2x(x+2)−5x−5(2)=0
2x(x+2)−5(x+2)=0
(x+2)(2x−5)=0
Now that the equation is written in , we will apply the .
(x+2)(2x−5)=0
x+2=02x−5=0(I)(II)
x=-2x=25
We can see that
x=25 and
x=-2 are solutions to the equation. However, recall that
x represents width. Since it does not make sense to have a negative value as a width,
x=25 is the only correct value. Now that we have width, we can solve for length.
We have found that the width of the rectangle is
25 feet and the length is
4 feet.