Answer: 2x^2 + 20x + 18
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