Algebraic Proof for x in a Right Triangle: PS, SR, and RP on a Straight Line

[Natasha1]

Homework Statement

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

Homework Equations

and attempt at a solution[/B]

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

 

[SteamKing]

Homework Statement

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

Homework Equations

and attempt at a solution[/B]

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

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.

 

[Natasha1]

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

 

[HallsofIvy]

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.

 

[ehild]

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

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

 

[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

 

[ehild]

well done!