The length of a room is 20m and its breadth is 5m. The sum of the areas of floor and the ceiling is equal to the area of the four walls. Find the height of the room.

$4 m$

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$5 m$

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$6 m$

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$10 m$

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Solution

The correct option is A
$4 m$

Area of the floor $= l \times b = 20 \times 5 = 100 m^{2}$

Area of the roof $= l \times b = 20 \times 5 = 100 m^{2}$

Let the height of the room be $h$

Area of the walls $= 2 (l \times h) + 2 (b \times h)$

$= 2 (20 h + 5 h) = 50 h$

$\Rightarrow 50 h = 100 + 100$

$\Rightarrow 50 h = 200$

$\Rightarrow h = \frac{200}{50} = 4 m$

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The length of a room is 20m and its breadth is 5m. The sum of the areas of floor and the ceiling is equal to the area of the four walls. Find the height of the room.

The correct option is A 4 m Area of the floor =l×b=20×5=100 m2 Area of the roof =l×b=20×5=100 m2 Let the height of the room be h Area of the walls =2(l×h)+2(b×h) =2(20h+5h)=50h ⇒50h=100+100 ⇒50h=200 ⇒h=20050=4 m