Question

A rectangle with length 2x-1 and width

x + 5 has an area of 156 square units. Find x.

Answer Choices
9
13
7 or 23/3
12​

Answer 1

The formula for the area of a rectangle is:

A = Length x Height

What we know:

Area = 156

Length = 2x - 1

Height = x + 5

^^^Plug these into the formula given above

156 = (2x - 1) × (x + 5)

156 = (2x - 1)(x + 5)

To solve this let's FOIL (2x - 1) and (x + 5)

FOIL (First, Outside, Inside, Last) like so

First:

(2x - 1)(x + 5) = 156

2x * x

2x²

Outside:

(2x - 1)(x + 5) = 156

2x * 5

10x

Inside:

(2x - 1)(x + 5) = 156

-1 * x

-x

Last:

(2x - 1)(x + 5) = 156

-1 * 5

-5

Now combine all the products of the FOIL together like so...

2x² + 10x + (-x) + (-5) = 156

2x² + 10x - x - 5 = 156

2x² + 9x - 5 = 156

2x² + 9x - 161 = 0

To find what x is you can use the quadratic equation to solve this (quadratic equation in image below)

Remember that quadratic functions are set up like so:

`ax^(2) +bx +c = 0`

That means that in this equation...

a = 2

b = 9

c = -161

^^^Plug these numbers into the quadratic equation and solve...

`\frac{-9+/-\sqrt{(9)^(2)-4(2)(-161)}}{2(2)}`

`(-9 +/-√(81+1288))/(4)`

`(-9+/-√(1369))/(4)`

`(-9+/-37)/(4)`

Keep in mind that +/- is ±

`(-9+37)/(4)` = 7

`(-9-37)/(4)` = -23/2 <<< You can't have a negative length so it will just be 23/2. Also, I believe that you made an error and wrote 23/3 instead of 23/2 :)

Hope this helped!

~Just a girl in love with Shawn Mendes