A wire is attached to the top of a pole. Question in description!

Question

A wire is attached to the top of a pole. The wire is 3ft longer than the pole, and the distance from the wire on the ground to the bottom of the pole is 3ft less than the height of the pole. Find the length of the pole and the height of the pole?

 

The Length of the wire is:

The height of the pole is:

Answer 1

This sounds like a Pythagorean problem. Let's write down what we know:

a² + b² = c² where a is the pole length, b is the length along the ground, and c is the wire

c = a + 3

b= a - 3

 

Since we have values for b and c, let's put them into our equation:

a² + (a - 3)² = (a + 3)²

Multiply out:

a² + a² - 6a + 9 = a² + 6a + 9

 

Now we start moving everything to one side. one of the a² cancel out:

a² - 6a +9 = 6a + 9

And the 9s cancel out:

a² - 6a = 6a

Move the 6a over as well:

a² - 12a = 0

 

Now we can factor:

a(a - 12) = 0

a = 0, 12

 

We can't have a length of 0, so the a-value has to be 12:

c = 12 + 3

c = 15

b = 12 - 3

b = 9

 

Now let's check:

12² + 9² = 15²

144 + 81 = 225

225 = 225