A ladder is placed in a hall resting against a wall reaching 7.5ft
above the ground. Keeping its foot at the same point, the ladder is
turned to the opposite wall to reach 12 ft above the ground. Find the
width of the hall, if the ladder is 12 feet long.
Answers
Given : A ladder is placed in a hall resting against a wall reaching 7.5f
above the ground. Keeping its foot at the same point, the ladder i
turned to the opposite wall to reach 12 ft above the ground.
ladder is 12 feet long.
or
ladder is 12.5 feet long.
To Find : the width of the hall
Solution:
Ladder length = Hypotenuse = 12 ft
A ladder is placed in a hall resting against a wall reaching 7.5ft
=> Perpendicular = 7.5 ft
Distance of foot of ladder from one side wall = x = Base
Base² = Hypotenuse² - Perpendicular²
=> x² = 12² - 7.5²
=> x² = (19.5)(4.5)
=> x² = 87.75
=> x = 9.367
other sides height = 12
=> Distance of foot of ladder from other side wall = √12² - 12² = 0
Hence width of Hall = 9.367 + 0 = 9.367 feet
Ladder 12.5 feet long
width of Hall =√ (12.5² - 7.5² ) + √ (12.5² - 12² )
= √ (20* 5 ) + √ (24.5*0.5 )
= √ 100 + √12.25
= 10 + 3.5
= 13.5
width of Hall = 13.5 feet
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Answer:
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