Question

An L shaped sidewalk from the library to the gym on a high school campus is 70 yards long. By cutting diagonally across the grass students shorten the walking distance to 50 yards. What are the lengths of the two legs of sidewalk?

Answer 1

30 and 40

Explanation:

That L-shaped sidewalk and the shortcut through the grass form a triangle, a rectangle triangle.

The shortcut represents the hypotenuse, and the two other sides sum up to 70 yards.

What's the relationship between the hypotenuse of a rectangle triangle and the other sides?

c² = a² + b²

So, we have here:

50² = a² + b²

50² = 2500

What are 2 numbers that are square numbers and added together make 2500? (think 25 it's easier and same principle)

How about 1600 and 900?

So, 2500 = 1600 + 900, or 50² = 40² + 30²

so the two sides legs of the sidewalk measure 30 and 40 yards.