Question

A piece of wire measuring 20 feet is attached to a telephone pole as a guy wire. The distance along the ground from the bottom of the pole to the end of the wire is 4 feet greater than the height where the wire is attached to the pole how far up the pole does the guy wire reach? PLEASE SHOW ALL WORK !!!!

Answer 1

Answer: Height at which the wire is attached to the pole is 12 feet.

Explanation:

Since we have given that

Length of the wire = 20 feet

Let the height at which wire is attached to the pole be h

and distance along the ground from the bottom of the pole to the end of the wire be x+4

Now, it forms  a right angle triangle so, we can apply "Pythagorus theorem".

$H^2=B^2+P^2\\\\20^2=x^2+(x+4)^2\\\\400=x^2+x^2+8x+16\\\\400=2x^2+8x+16\\\\400=2(x^2+4x+8)\\\\200=x^2+4x+8\\\\x^2+4x-192=0\\\\x^2+16x-12x-192=0\\\\x(x+16)-12(x+16)=0\\\\(x+16)(x-12)=0\\\\x=-16\ and\ 12$

But height cant be negative so, height will be 12 feet.

Hence, height at which the wire is attached to the pole is 12 feet.