# Pythagoras and algebra

1. Mar 21, 2016

### Natasha1

• Member warned about posting with no effort shown
1. The problem statement, all variables and given/known data
In a diagram, P, Q and R lie on a straight line and angle SQR is a right angle. The lengths PS, SR and RP are a, b and c cm respectively and QR is x cm.

Use algebra to show that x = (b^2 + c^2 - a^2) / 2c

2. Relevant equations and attempt at a solution

Do I need to use Pythagoras for this question? I need a prompt, a little help please...

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Last edited: Mar 21, 2016
2. Mar 21, 2016

### SteamKing

Staff Emeritus
Beats me. Do you have a diagram to refer to? If not, you should make one, based on the description of the points.

Since there is a right angle involved, I would keep Pythagoras handy, nevertheless.

3. Mar 21, 2016

### Natasha1

I have attached a picture of the triangle in question... Hope it worked...

4. Mar 21, 2016

### HallsofIvy

Staff Emeritus
Drawing a line from the right angle perpendicular to the hypotenuse divides the original right angle into two triangles both similar to the original triangle.

5. Mar 22, 2016

### ehild

Yes, you can solve the problem by using Pythagoras' Theorem for both the yellow and blue triangles.

6. Mar 22, 2016

### Natasha1

Got it!
After some working I got...

a^2 - c^2 +2cx -x^2 = b^2 - x^2
which simplifies to:
x = (b^2 + c^2 - a^2) / 2c

Thanks ehild I equated the m

7. Mar 23, 2016

well done!