Question

The area of a rectangular garden is given by the trinomial x + x - 30. What are the possible

dimensions of the rectangle? Use factoring.
(x-6) and (x - 5)
(x + 6) and (x - 5)
(x + 6) and (x + 5)
(x - 6) and (x + 5)

Answer 1

The possible dimensions of the rectangle are (x+6) and( x- 5)

Explanation:

The area of the rectangle is given as
`x^(2)  + x-30`

Now, Area of Rectangle = Length x Breadth

So, we need to factorize the given polynomial to find the dimensions of garden.

`x^(2)  + x-30 = x^(2)  + 6x - 5x - 30`

or,
`x^(2)  + 6x - 5x - 30 = x(x+6)-5(x+6) = (x+6)(x-5)`

or,
`x^(2)  + 6x - 5x - 30 = (x+6)(x-5)`

So, the factors of the given polynomial are (x+6) and( x- 5)

Hence, the possible dimensions of the rectangle are (x+6) and( x- 5)