contestada

The length of a cinema hall is 20 m and breadth is 16 m. The sum of the areas of floor and flat roof is equal to the areas of four walls. Find the height of the hall.
A.8.9 m
B.9.1 m
C.7.24 m
D.7.5 m

Respuesta :

mhanifa

A. 8.9 m

==============

Equate the sum of the areas of the floor and the roof to the combined area of the four walls.

Given the measurements, the floor and the roof are both rectangles with a length of 20 m and a breadth of 16 m.

Area of the floor (or roof) is:

  • Length × Breadth = 20 × 16 = 320 m²

Since the sum of the areas of the floor and flat roof is equal to the combined area of the four walls.

Combined area of the floor and roof is:

  • 2 × 320 m² = 640 m²

The area of the four walls can be calculated by adding together the areas of all individual walls.

There are two pairs of opposite walls: one pair with a height 'h' and a length of 20 m (front and back), and another pair with a height 'h' and a length of 16 m (sides).

Area of the four walls is:

  • 2 × (20 × h) + 2 × (16 × h) = 2h × (20 + 16) = 2h × 36 = 72 h

Now we set the combined area of the four walls equal to the combined area of the floor and roof:

  • 72 h = 640

So the height can be found as follows:

  • h = 640 / 72  ≈  8.89 m

Therefore, the height of the hall is roughly 8.9 m, so the correct answer is A. 8.9 m.

Otras preguntas