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

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Homework Help Overview

The problem involves a geometric configuration where points P, Q, and R are collinear, and angle SQR is a right angle. The lengths PS, SR, and RP are given as a, b, and c cm, respectively, with the goal of expressing QR, denoted as x, in terms of these lengths using algebra.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss the potential use of Pythagoras' Theorem in solving the problem. Some suggest creating a diagram to better visualize the relationships between the points and lengths involved. There are mentions of dividing the right triangle into smaller similar triangles to aid in the reasoning.

Discussion Status

The discussion has progressed with participants sharing insights and confirming the use of Pythagoras' Theorem as a viable approach. One participant has articulated a derived equation related to the problem, indicating a productive direction in the exploration of the solution.

Contextual Notes

There are references to the necessity of a diagram for clarity, and the discussion includes considerations of the relationships between the sides of the triangles involved. The original poster expresses a need for guidance, indicating a level of uncertainty in their approach.

Natasha1
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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...
 

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Natasha1 said:

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.
 
I have attached a picture of the triangle in question... Hope it worked...
 
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.
 
Natasha1 said:
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.

upload_2016-3-22_6-32-52.png
 
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Likes   Reactions: 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
 
well done!
 

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