You need two bottles of fertilizer to treat the flower garden shown. How many bottles do you need to treat a similar garden with

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.