Question

40. Area of four walls of a room is 77 m2 and its length and breadth are 7.5 m
and 3.5 m respectively. The height of the room is:
(a) 3.5 m
(b) 5.4 m
(c) 6.77 m
(d) 7.7 m
dth and height of the room is
​

Answer 1

• a) Option is correct beacuse height of room is 3.5 m.

Step-by-step explanation:

Given:-

• Area of four walls of room is 77 m².
• Length of room is 7.5 m.
• Breadth of room is 3.5 m.

To find:-

• Height of room.

Solution:-

• We know that Area of four walls is given. Then Area will be Lateral surface area.

• Length and Breadth of room is given. Then the room is of cuboidal shape.

We know that,

Lateral surface area of cuboid = 2(l +b) h

In which,

• l is length of cuboid.
• b is breadth of cuboid.
• h is height of cuboid.

L.S.A = 77 m²

l = 7.5 cm.

b = 3.5 cm .

Put all values in formula :

➜ 77 = 2 × (7.5 + 3.5) × h

➜ 77 = 2h (7.5 + 3.5)

➜ 77 = 15h + 7h

➜ 77 = 22h

➜ 77/22 = h

➜ 3.5 = h

Or, h = 3.5

Verification:-

➜77 = 2 × (7.5 + 3.5) × h

➜ 77 = 2h (7.5 + 3.5)

• Put h = 3.5

➜ 77 = 2 × 3.5 (7.5 + 3.5)

➜ 77 = 7 (7.5 + 3.5)

➜ 77 = 52.5 + 24.5

➜ 77 = 77

Hence, Verified.

Therefore,

Height of room is 3.5 m.