Question 374277
Yes, this is correct.


The guy wire, the telephone phone and the ground form a right-angled triangle.
Your measurements are x, x+4, and 20.
To solve for x, you could use the Pythagorean Theorem, {{{a^2+b^2=c^2}}}.


Let a=x
Let b=x+4
Let c=20


First, plug in the values for a, b and c, and then simplify.
{{{x^2+(x+4)^2=20^2}}}
{{{x^2+x^2+8x+16=400}}}
{{{2x^2+8x-384=0}}}


From here, solve for x by either factoring, or using the quadratic formula (I'm going to use the quadratic formula).

{{{x =(-b+-sqrt(b^2-4ac))/(2a)}}}
{{{x =(-(8)+-sqrt((8)^2-4(2)(-384)))/(2(2))}}}
{{{x=(-8+-sqrt(3136))/4}}}
{{{x=(-8+sqrt(3136))/4}}} or {{{x=(-8-sqrt(3136))/4}}}
x=12 or -16


Now, plug in the values of x into the original formula ({{{x^2+(x+4)^2=20^2}}}})
{{{x^2+(x+4)^2=20^2}}}
{{{12^2+(12+4)^2=20^2}}}
144+256=400
400=400


{{{x^2+(x+4)^2=20^2}}}
{{{(-16)^2+((-16)+4)^2=20^2}}}
256+144=400
400=400


By just looking at the numbers, you could conclude that both values of x could be correct. However, we have to look back to our word problem.

The measurement of the telephone pole is x.
Our values of x are 12 and -16.
If we substitute the values of x in,
only x=12 makes sense,
because a telephone pole with height -16 is impossible unless you're measuring from a reference point 16ft above one end of it.