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The length of a hall is $18 m$ and the width is $12 m$ . 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 wall.

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7.2m

6.2m

7.8m

1.8m

answer is A.

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Detailed Solution

It is given the length of a hall is 18 m and the width is 12 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.
Calculate the area of the floor,

A = l b ⇒ A = 18 × 12 ⇒ A = 216 m 2

Calculate the total area of the roof and floor,

T o t a l A r e a = 216 + 216 ⇒ T o t a l A r e a = 432 m 2 .......... 1

Calculate the area of the walls,

A W = 2 l h + b h .......... 2

Comparing the equations

1

and

2

2 l h + b h = 432

Substituting the values,

2 h 18 + 12 = 432

Simplifying the term,

60 h = 432

Divide both sides by 60,

h = 43260

⇒ h = 7.2 m

So, the height of the wall is 7.2

m

.
Hence option (1) is correct.

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