Problema Solution
a 40 meter ladder and a 30 meter ladder were leans against a building. the bottom of the longest ladder was 14 meters farther from the building than the bottom of the shorter ladder, but both ladders reached the same distance up the building. find the distance the ladders reached up the building.
Answer provided by our tutors
let
h = the distance the ladders reached up the building, h>0
x = the distance of the bottom of the shorter ladder from the wall, x>0
x + 14 = the distance of the bottom of the longest ladder from the wall
make a good drawing and notice the right triangles that the ladders make with the wall
using the Pythagorean Theorem we have
h^2 = 30^2 - x^2
h^2 = 40^2 - (x + 14)^2
that is
40^2 - (x + 14)^2 = 30^2 - x^2
by solving we find
x = 18 m
click here to see the step by step solution of the equation
h^2 = 30^2 - 18^2
h = 24 m
the distance the ladders reached up the building is 24 meters.