Solve the problem.
-A 12-foot pole is supported by two wires that extend from the top of the pole to points that are each 5 feet from the base of the pole. Find the total length of the two wires.
A) 13 ft
B) 26 ft
C) 338 ft
D) 34 ft

Question

Quizplus · Accepted Answer

We can use the Pythagorean theorem to find the length of each wire. Let's call the wires A and B.

For wire A: 
a^2 + b^2 = c^2 
a^2 + 5^2 = 12^2 
a^2 = 144 - 25 
a = sqrt(119)

For wire B: 
a^2 + b^2 = c^2 
b^2 + 5^2 = 12^2 
b^2 = 144 - 25 
b = sqrt(119)

The total length of the wires is the sum of their lengths: 
A + B = sqrt(119) + sqrt(119) 
A + B = 2sqrt(119)

We can leave the answer in this form, or we can calculate an approximate decimal value: 
A + B ≈ 2(sqrt(120)) ≈ 2(10.95) ≈ 21.9

Either way, the answer is closest to choice B, 26 ft. We can use the Pythagorean theorem to find the length of one of the wires: 
$5^2 + 12^2 = x^2$
Simplifying this equation gives: 
$x^2 = 169$
Taking the square root of both sides gives: 
$x = 13$
Since there are two wires, the total length is 2 times 13, which equals 26 feet. So the answer is B.

Solve the Problem. -A 12-Foot Pole Is Supported by Two Wires That Extend