Applications of Pythagoras' Theorem in Real-World Contexts

Question

A folded napkin has a triangular cross section of sides x cm, (x+1) cm and (x+2) cm. If one of the angles of the triangle is 90°, find the value of x.

Answer 1

x² + (x+1)² = (x+2)²

X² - 2x - 3=0

One root is extraneous and the other is 3 which gives 3,4 & 5 for the sides.

This is a well known right triangle as required.

Added:

I'm not sure how much additional process I should need to include.

You should know how to expand the initial equation (use FOIL) and then collect terms to get

the simplified equation I gave you.

That equation factors easily enough that you should know how to do it.

Then you are done.

Answer 2

(x + 2)² = x² + (x + 1)²

Solve for x using Algebra 1 techniques.