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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

 Jan 16, 2019
 #1
avatar+96201 
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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

 

 

cool cool cool

 Jan 16, 2019

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