Question

If the area of a rectangle is 12, the length is x-1, and the width is 2x+3, how would you find X?

Answer 1

`x = 2.5`

Explanation:

Given:
The area of a rectangle is 12,
The length is x-1, and
The width is 2x+3.

To find: x = ?

Area of rectangle = Length`\times`width

`12 = (x-1)\times (2x+3)`

`12 = (x (2x+3) - 1(2x+3))`

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

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

Transposing 12:

`2x^2 +x -3 -12 = 0`

`2x^2 +x -15 = 0`

Factorise:

`2x^2 +6x-5x -15 = 0`

`2x(x +3) -5 (x +3) = 0`

# (2x-5)(x+3) =0

So

`(2x-5)=0 => (2x =5) => x=5/2`
Or
`(x+3) = 0=> x=-3`

As we cannot have negative length, we take `x = 5/2 = 2.5`

Ans : `x = 2.5`