Respuesta :
Answer: height = 10 feet
Base = 24 feet
Step-by-step explanation:
Let h represent the height of the triangular flower bed.
Let b represent the base of the triangular flower bed
The formula for determining the area of a triangle is expressed as
Area = 1/2 × base × height
The area of a triangular flower bed in the park has an area of 120 square feet. This means that
1/2 × bh = 120
bh = 120 × 2
bh = 240- - - - - - - - - - - - - - - 1
The base is 4 feet longer than twice the height. This means that
b = 2h + 4
Substituting b = 2h + 4 into equation 1, it becomes
h(2h + 4) = 240
2h² + 4h = 240
2h² + 4h - 240 = 0
Dividing through by 2, it becomes
h² + 2h - 120 = 0
h² + 12h - 10h - 120 = 0
h(h + 12) - 10(h + 12) = 0
h - 10 = 0 or h + 12 = 0
h = 10 or h = - 12
Since the height cannot be negative, then h = 10
Substituting h = 10 into equation 1, it becomes
10b = 240
b = 240/10
y = 24
