Question

The length of a rectangle is 3 inches less than twice the width. The area is 65 square inches. Find the length and width

Answer 1

How would you set this problem up using x as a variable for the width?

Answer 2

I have no idea

Answer 3

Your first sentence gives you all you need: the length is 3 less (subtraction) than twice (multiplication) the width. So if you multiply the width by two (2x), then what would you do?

Answer 4

I'm not sure

Answer 5

x=13/2

Answer 6

width = x
length = 2x - ?
Area = length * width

Answer 7

3?

Answer 8

Yup! length = 2x - 3
Now, you plug in these values for length and width into the equation for area:
Area = length * width
Area = (2x - 3) (x)
distribute the x and what do you get?

Answer 9

How do I distribute?

Answer 10

(x*2x) - (x*3)

Answer 11

3x-3x?

Answer 12

Close, \[2x^2-3x\]
because \[x \times x=x^2\]

Answer 13

Now plug in your given value for Area (65):

\[65=2x^2-3x\]
and solve for x

Answer 14

How do I solve that?

Answer 15

2x^2-3x+65=0?

Answer 16

Almost, subtract 65 from both sides to get zero on one side
\[0=2x^2-3x-65\]

Answer 17

65-65=0

Answer 18

Okay. But what do I do now?

Answer 19

Kinda hard to explain, but here
http://www.purplemath.com/modules/solvquad4.htm

Answer 20

Thank you

Answer 21

No problem! :)