126k views
1 vote
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​

1 Answer

2 votes

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

A rectangle with length 2x-1 and width x + 5 has an area of 156 square units. Find-example-1
User Macil
by
8.5k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories