Posted by **Jane** on Tuesday, April 2, 2013 at 11:04am.

A walking path is shaped like a rectangle with a width 7 times its length "l". What is a simplified expression for the distance between opposite corners of the walking path?

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**Wayne**, Tuesday, April 2, 2013 at 12:31pm
Did you draw a picture? The distance between opposite corners of the walking path (rectangle, in this case) would be the hypotenuse of a right triangle. Thus, we can use the Pythagorean Theorem: HYP^2 = leg^2 + leg^2

Let x = length; 7x = width, so

HYP^2 = x^2 + (7x)^2

HYP^2 = x^2 + 49x^2

faactor out x^2:

HYP^2 = x^2 * (1+49)

HYP^2 = X^2 * 25 * 2

square root both sides

HYP = 5x * sqrt(2)

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