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?

w√26

Step-by-step explanation:

A rectangle is a four sided shape with 4 perpendicular angles. It has two pairs of parallel sides which are equal in distance: width and length. The width here is w and the length is 5w or 5 times the width. A diagonal can be drawn between opposite corners that splits the triangle into two equal right triangles. The distance of this diagonal is found using the Pythagorean Theorem a² + b² = c². In the rectangle a = w and b = 5w. Substitute these values and simplify using a square root operation.

w² + (5w) ² = c²

w² + 25w² = c²

26w² = c²

√26w² = c

w√26 = c