Question

marla needs 2 ropes to anchor each 7-foot pole, as shown in the diagram. diagram: vertical pole labeled 7 ft, horizontal distance from pole to rope anchor labeled 3.5 ft marla plans to add 2 feet to the length of each rope so she has enough rope to tie knots. how much rope does marla need to anchor both poles?
a. 26.33 feet
b. 31.32 feet
c. 32.25 feet
d. 39.32 feet

Explanation:

Step1: Find length of one rope (without knot)

Using Pythagorean theorem: \( c = \sqrt{a^2 + b^2} \), where \( a = 7 \), \( b = 3.5 \).
\( c = \sqrt{7^2 + 3.5^2} = \sqrt{49 + 12.25} = \sqrt{61.25} \approx 7.826 \) ft.

Step2: Add 2 ft for knot to one rope

Length of one rope with knot: \( 7.826 + 2 = 9.826 \) ft.

Step3: Ropes per pole and total poles

Each pole needs 2 ropes, 2 poles: \( 2 \times 2 = 4 \) ropes total.

Step4: Total rope length

Total length: \( 9.826 \times 4 \approx 39.304 \approx 39.32 \) ft.

Answer:

D. 39.32 feet