Question

The area of a rectangle is represented by the polynomial x^2+3x-6x-18. What are the length, width, and area of the rectangle if x=12?

Answer 1

Length = 15

Width = 6

Area = 90

Explanation:

Area of the rectangle =
`{x}^(2) + 3x - 6x - 18`

Lets factorise the polynomial

`= > x(x + 3) - 6(x + 3)`

`= > (x + 3)(x - 6)`

We know that Area = Length × Width

Let the length be (x + 3) & width be (x - 6)

Its given in the question that x = 12. So putting the value of x gives ,

Length =
`x + 3 = 12 + 3 = 15`

Width =
`x - 6 = 12 - 6 = 6`

Area = Length × Width = 15 × 6 = 90