Question : 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.
Option 1: 8.4 m
Option 2: 8.2 m
Option 3: 8.6 m
Option 4: 8.8 m
Correct Answer: 8.4 m
Solution :
Let the height of the hall be $h$ m.
Now, the area of the floor = the area of the roof = (21 × 14) = 294 m
2
.
The sum of the areas of the four walls = 2 × (length + breadth) × height
= 2 × (21 + 14) × $h$ m
2
.
According to the question,
2(21 + 14) × $h$ = 294 + 294
⇒ $70h$ = 588
⇒ $h=\frac{588}{70}$ = 8.4 m.
Hence, the correct answer is 8.4 m.
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