A 22m ladder and a 20m ladder were leaned against a building. The bottom of the longer ladder was 4m farther from the building than the bottom of the shorter ladder, but both ladders reached the same distance up the building. Find this distance to the nearest tenth.
b. 19.2m
c. 18.1m
+128475 We have this equation
22^2 - ( d + 4)^2 = 20^2 - d^2 where d is the distance that the shorter ladder is from the bldg
Simplify
484 - d^2 - 8d - 16 = 400 - d^2
468 - 8d = 400 rearrange as
468 - 400 = 8d
68 = 8d
17 = 2d
d = 17/2 = 8.5 m
So.....the distance that both ladders reach up the bldg =
sqrt [ 400 - 8.5^2 ] = 18. 1 m
