Rug in a room, pythagoras ?

Kieran

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Nov 16, 2012
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A room measures 11*10 units. A rug fits diagonally into the room and touches the 4 walls. It's length is double it's width. What are the dimensions of the rug ? I drew a diagram and let 11-n, 10-c and 2x represent the values of the triangle newly formed. 2x represents the hypotenuse. I worked with another triangle , the three sides are represented by n, c and x the latter is the hypotenuse . Again , use pythagoras and solve for the 2 equations that = a common x value, say 4x sqrd. Am I on the correct road ? Cheers.
 
Am I on the correct road ?

Yes, it seems so.

You've introduced three variables (x, n, c), so you'll need to write a system of three equations.

You have a rectangle that measures 2x by x.

You have two right triangles with hypotenuse x and legs n and c.

You have two right triangles with hypotenuse 2x and legs (11-n) and (10-c).

The areas of these five objects must add up to the area of the room (which you know).

That's one equation.

Two additional equations come from expressing the Pythagorean Theorem, using the dimensions of the two triangles.

After that, it's some basic algebra to solve the system of three equations.

If you need more help, please show us how far you got, so that we may check your work.

Cheers :cool:
 
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