Question

A wall paper 312 m long and 25 cm wide is required to cover the walls of a room. length of the room is 7 m and breath is twice its height. determine the height of the room.

Answer 1

Answer:

The height of room is 3 meters .

Step-by-step explanation:

Given as :

The length of wall paper = L = 312 m = 31200 cm

The width of wall paper = B = 25 cm

The length of room = l = 7 m

The breadth of room = b = 2 × height

Let The height of room = h meters

According to question

Area of wall paper = L × B

Or, Area of wall paper = 31200 cm × 25 cm

Or, Area of wall paper = 780000 cm²

i.e Area of wall paper = 78 m²

Again

Area of four wall of room = 2 × (length + breadth) × height

i.e Area of four wall of room = 2 × (l + b) × h

Or, Area of four wall of room = 2 × (7 meter + 2 h) × h

Or, Area of four wall of room = (14 + 4 h) × h

Or, Area of four wall of room = 14 h + 4 h²

Again

Since The wall paper is printed on four wall room

So, Area of four wall of room =  Area of wall paper

i.e  14 h + 4 h² = 78

Or, 4 h² + 14 h - 78 = 0

Or, 2 h² + 7 h - 39 = 0

Solving this quadratic equation

2 h² - 6 h + 13 h - 39 = 0

Or, 2 h (h - 3) + 13 (h - 3) = 0

Or, (h - 3) (2 h + 13) = 0

i.e h - 3 = 0  and  2 h + 13 = 0

So, h = 3  , h = $\dfrac{-13}{2}$

So, The height of room = h = 3 meters

Hence, The height of room is 3 meters . Answer