The area of rectangle is 80. The lengths is two more than the width. Find the dimensions

Answer 1

-First, some guidelines to work out these types of problems:

1. Draw a picture and label it
2. relate the variables and numbers to each other in a way that makes sense with the story of the word problem
3. Solve

-Draw a picture

It should be a rectangle with the longer side labeled "w+2" (the length is 2 more than the width) and the shorter side labeled "w" (width)

-Relate the variable and numbers

Area is 80 -> A = 80

Length = w + 2

Width = w

Area of a rectangle is length times width -> A = lw

-Solve. Now, we just plug in what we know about each of these variables and solve:

A = lw

80 = (w +2 ) (w)

80 = w^2 + 2w

0 = w^2 + 2w - 80

w^2 + 2w - 80 = 0 <-- I just flipped it around because it's easier to understand this way

(w + 10) (w -8) = 0 <--when you have a quadratic, you must factor in order to solve for "w"

w = -10 and w = 8

We only use w=8 because -10 is not a possible width (we do not measure length in terms of negatives!)

Now that we know the width, let's find the length. *Remember, from before Length = w + 2

Length = 8 + 2

Length = 10

-The final answer:

Your dimensions are -> width = 8 and length = 10

You did it!