Question

The area of a garden is given by the trinomial of g2-2g-24.the garden's length is g+4. what is the garden's width

Answer 1

The width of the garden is g-6

Answer 2

width of the garden's is, g-6 unit

Explanation:

Area of rectangle(A) is given by:

`A = lw`

where

l is the length of the rectangle

w is the width of the rectangle.

As per the statement:

The area of a garden is given by the trinomial of
`g^2-2g-24` and the garden's length is g+4

⇒
`A = g^2-2g-24` square units and
`l = g+4` units

Factorize
`g^2-2g-24`

`g^2-6g+4g-24 = g(g-6)+g(g-6)`

⇒
`(g+4)(g-6)`

⇒A =
`g^2-2g-24=(g+4)(g-6)`

Substitute these in [1] we have;

`(g+4)(g-6)=(g+4) \cdot w`

Divide both sides by g+4 we have;

⇒
`g-6 = w`

Therefore, the width of the garden's is, g-6 unit