Question

A park is shaped like a rectangle with a length 5 times its width w. What is a simplified expression for the distance between opposite corners of the​ park

Answer 1

if the width is w
and the length is 5 times the width, then the length is naturally 5*w

if we draw the distance between opposite corners of the park, we can see that the rectangle is now made up of two right triangles with legs w and 5w, and an unknown hypotenuse

let the unknown distance be x

use the pythagorean theorem to write out the unknown distance with respect to w

recall: a^2 + b^2 = c^2 where a and b are the legs, and c is the hypotenuse, of a right triangle