# Thread: Using Pythagorean theorem twice

1. ## Using Pythagorean theorem twice

There is a problem I don't know how to solve, only that you are going to use the Pythagorean theorem twice.

From a house, there are two small roads to a bigger main road. The two roads are 1 and 2 km. The distance along the main road between the two road's connections with it is 1.5 km. You want to plan for a new road from the main road to the house. You want the new road to become as short as possible. How long will this road be?

2. ## Re: Using Pythagorean theorem twice

Hey EulerWannabe.

Have you tried drawing a diagram?

3. ## Re: Using Pythagorean theorem twice

HINT:
this will "create" 2 right triangles
use Big Pete Pythagoras' formula on both

4. ## Re: Using Pythagorean theorem twice

Two right triangles ... two equations

$x^2+y^2=1^2$

$(x+1.5)^2 + y^2 = 2^2$

5. ## Re: Using Pythagorean theorem twice

The posts above show you the mechanics.

But to realize why those are the correct mechanics, you have to remember that the shortest distance between a line and a point not on that line is measured along a line that includes the given point and is perpendicular to the given line.

6. ## Re: Using Pythagorean theorem twice

Thank you so much and sorry for not giving you more information on what I had done before. I did already draw a diagram but I tried to solve it with only one variable. Ended up with the the following fantastic equality: 4 = 4. Not very exciting. xD
Thanks again!