Response:
26.25 bottles
Detailed explanation:
The trapezoidal flower garden is depicted. The longer base measures 18 feet, the shorter base is 15 feet, the height is 4 feet, and one side measures 5 feet.
The formula for the perimeter of a trapezoid is: Side a + side b + length a + length b
For the trapezoid in question, to calculate the perimeter, first, we identify the missing length
Length a
Height is given as 4 feet
Longer base length = 18 feet
Shorter base length = 15 feet
The difference will determine the base of the right triangle
= 18 - 15 = 3 feet
Using the Pythagorean theorem allows us to calculate side a = c
a² + b² = c²
3² + 4² = c²
9 + 16 = c²
c = √25
c = 5 feet
Therefore, side a = 5 feet
The perimeter of the trapezoid is calculated as:
18 feet + 15 feet + 5 feet + 5 feet
= 38 feet.
The question states,
It's necessary to use 2 bottles of fertilizer for the flower garden shown. Determine how many bottles are needed for a similar garden with a perimeter of 105 feet
Thus:
38 feet = 2 bottles
105 feet = x bottles
Cross multiplying yields
= 38 × x = 105 × 2
= 38x = 210
x = 210 / 38
x = 26.25 bottles
To treat the garden with a perimeter of 105 feet, 26.25 bottles of fertilizer are required.