Question

1. the area of the two side  walls of a room is 5250m^2 and the area of two end walls 4550m^2
and the area of the floor is 4875m^2. Find the dimensions of the room.
(the ans is 75m , 65m,35m but i hv no idea hw to het the answer please answer with exact steps leading to the answer) whoever answers first will get the best ans plsss....

2. a room 8m long, 6m broad and 3m high has two windows 1 1/2m*1m and a door 2m*1 1/2m. FInd the cost of papering the  walls with paper 50 cm wide at rs 40 per. metre 
(ans: rs 6240)

Answer 1

1)

Let us say we are at the door of the room in the front. Let us say the distance from the door to the far end of the room is = L meters = length.  Let us say the distance between the two side walls is width = W meters.  Let us denote the height of the room by H meters.

Combined area of two side walls = 2 LH = 5250 m² ,
               L H = 2625 m²   -- eq 1  
Combined area of two end walls (front and rear walls) = 2 WH = 4550 m²
                   W H = 2275 m²   -- eq 2
Area of floor = L W = 4875 m²       -- eq 3

divide eq 1 by eq 2:   LH/WH = 2625/2275.   L = (2625 W / 2275)
Putting this value in eq 3,   2625 W²/2275 = 4875 

         W = √(4875*2275/2625) = √4225 = 65 meters

Substitute this in eq 2 :   H = 2275/65 = 35 m
Substitute this in equ 1   L = 2625/35 = 75 m

So the dimensions of the room are  75 m * 65 m * 35 m

2) 

Area of both side walls = 2 * length * height = 2*8*3 = 48 m²
Area of front and rear walls = 2 * width * height = 2 *6*3 = 36 m²
Area of two windows = 2 * 1.5 * 1 = 3 m²
Area of one door = 2 * 1.5 = 3 m²

Area of the four walls that is to be papered = 48+36-3-3 = 78 m²
Cost of wall paper = 78 m² * Rs 40 / (0.50 m * 1 m) = Rs 6, 240.