Problema Solution
You and a friend are walking together on a sidewalk to get to a particular location. The distance from the top of the sidewalk to the turn is 10 feet more than the distance from the turn to where you are going. If you cut across the lawn the distance from the top of the sidewalk to where you want to go is 40 ft. Approximate to the nearest foot how many feet of walking distance you and your friend could save by cutting across the lawn instead of walking on the sidewalk.
Answer provided by our tutors
Let
x = the distance from the turn to where you are going
x + 10 = the distance from the top of the sidewalk to the turn
Using the Pythagorean Theorem we have:
x^2 + (x + 10)^2 = 40^2
........
click here to see the equation solved for x
........
x = 22.84 ft
(x + x + 10) - 40 = (2x + 10) - 40 = 2x - 30 = 2*22.84 - 30 = 16 ft approximately
If you cut across the lawn you would save 16 feet walking distance.