The length of the top of a table is 22m greater than the width. The area is 80 m2. Find the dimensions of the table.

Question

need help with this word problem

Answer 1

I hope you started by drawing a picture.

 

A rectangle has a length (l) and a width (w), and the rectangle's area is the length times the width (l*w)

 

In this case, we don't know the width, so I'll just continue using w for the width. We know that the length is 22 units more than the width, so the length is really w+22.

 

Instead of the area being l*w, I can write it as (w+22)*w. Make sure to use parentheses when you do this! We also know that the area is equal to 80 units², so we have the equation (w+22)*w=80

 

Ok first, let's distribute on the left side: w²+22w=80

and subtract 80: w²+22w-80=0

 

This quadratic equation doesn't factor, so we can use the quadratic formula to solve from here - substitute a=1, b=22, and c=-80 into the formula w=(-b±sqrt(b²-4ac))/2a. Remember to disregard the negative root, since our width will not be a negative number!

Answer 2

Let w - the width

Let w + 22 = the length

A = lw

80 = w(w + 22)

80 = w² + 22w

0 = w² + 22w - 80    Use the quadratic formula.

w = -22 ±√[22² - 4(1)(-80)]

                 2(1)

w = -22 ±√[484 + 320]

                  2

w = -22 ±√804

               2

w ≈ -22 ± 28.35

               2

w ≈ 3.175 m

w + 22 ≈ 25.175 m