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Q.

A ladder 10m long rests against a vertical wall. If the foot of the ladder is 6m away from the wall and the ladder just reaches the top of the wall, how high is the wall?


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a

6m

b

8m

c

7m

d

9m 

answer is B.

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Detailed Solution

It is given that a ladder 10m long rests against a vertical wall, the foot of the ladder is 6m away from the wall and the ladder just reaches the top of the wall, it is required to find the height of the wall.
Pythagoras theorem:
In a right-angled triangle, the square of the hypotenuse side is equal to the sum of squares of the other two sides. If perpendicular side = a, base = b and hypotenuse = c then
c 2 = a 2 + b 2  
The length of the ladder is BC = 10 m and distance between wall and ladder is AC = 6 m as shown below.
Question ImageApply Pythagoras theorem to find the height of the wall.
Pythagoras theorem gives,
⇒A B 2 +A C 2 =B C 2  
⇒A B 2 + 6 2 = 10 2   ⇒A B 2 +36=100   ⇒A B 2 =100−36   ⇒A B 2 =64 ⇒AB=8  
The height of the wall, AB = 8 m.
Therefore, option 2 is correct.
 
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