Question

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?
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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