James typically walks 2 miles east on A Street and 1.5 miles north on B Street in order to get to Sarah's house. How much SHORTER would his walk be if he took the shortcut by taking C Street?
Answers
His walk would be Shorter by 1 Mile if he takes Street C.
Given in the question, James typically walks 2 miles east on A Street and 1.5 miles north on B Street in order to get to Sarah's house.
We have to find how much SHORTER would his walk be if he took the shortcut by taking C Street.
In the following figure we have a right triangle of A,B and C.
Here A is the base, B is the perpendicular and C is the hypotenuse.
By pythagoras theorem, we have:-
sqr(C) = sqr(A) + sqr(B).
where sqr denotes the square of sides.
Hence sqr(2) + sqr(1.5) = sqr(c),where c denotes length of side C.
Hence we get sqr(c) = 6.25.
=> c = 2.5.
Hence by taking Side A + Side B james covered the distance of 1.5 + 2 = 3.5 Miles.
While by taking the shortcut he covers the distance of side C = 2.5 Miles.
Hence by taking side C his walk becomes shorter by 3.5 Miles - 2.5 Miles =1 Mile.