Question

A rectangle has a length of (x+3), width of (x-4) and an area of 120. What is the perimeter of the rectangle?

a. 40
b. 42
c. 46
d. 48

Answer 1

Option C,
`46`

Explanation:

Step 1: Distribute

Formula →
`A = l * w`

`120 = (x+3) * (x-4)`

`120 = (x*x)+(x*-4)+(3*x)+(3*-4)`

`120 = x^2 - 4x + 3x - 12`

Step 2: Solve for x

`120 - 120 = x^2 - x - 12 - 120`

`0 = x^2 - x - 132`

`0 = (x - 12)(x + 11)`

`x = 12, -11`

Step 3: Determine the perimeter of the rectangle

`P = 2(l + w)`

`P = 2((12 + 3) + (12-4))`

`P = 2(15 + 8)`

`P = 2(23)`

`P = 46`

Answer: Option C,
`46`