Benjamin is doing some remodeling at his home. he currently has a triangular patio that has a base that is four times as long as its height. he wants to increase the length of the base of the patio by 4 feet and the length of the height of the patio by 9 feet. if x represents the height of the patio, which of the following functions will give the area of the new patio?

2x^2 + 20x + 18

Step-by-step explanation:

Let x represent the height of the patio.

He currently has a triangular patio that has a base that is four times as long as its height. This means that the length of the base of the patio is 4x.

He wants to increase the length of the base of the patio by 4 feet and the length of the height of the patio by 9 feet. This means that the length of the base of the new patio would be 4x + 4

Also, the height of the new patio would be x + 9

The formula for determining the area of a triangle is

Area = 1/2 × base × height

Therefore, the function representing the area of the new patio would be

1/2 × (4x + 4) × (x + 9)

= 1/2(4x^2 + 36x + 4x + 36)

= 1/2(4x^2 + 40x + 36)

= 2x^2 + 20x + 18