The length of a hall is 21 m and the width is 14 m. The sum of the areas of the floor and the flat roof is equal to the sum of the areas of the four walls. Find the height of the hall.
Show answer & explanation
Correct answer: A
Explanation
The correct answer is option 1 i.e. 8.4 m.
Let the height of the hall = h meters
Length of the hall l = 21 meters
Width of the hall w = 14 meters
The area of the floor (or roof) = l × w = 21 × 14 = 294 m2
The total area of the floor and the roof = 2 × 294 = 588 m2
Area of the four walls and roof= 2(w × h + h × l) = 2(14 × h + h × 21)
⇒ 2 × 35h = 70h
According to the question,
the sum of the areas of the floor and roof is equal to the sum of the areas of the four walls:
⇒ 588 = 70h
⇒ h = 588/70 = 8.4 m