Question

The length of a room is 50per cent more than its breadth. The cost of carpeting the room @ of rupees 38.50m square is rupees 924 and the cost of painting the walls @ of rupees 5.50 per m square is rupees 1320. Find the dimensions of the room.

Answer 1

Heya ☺

Let the breadth of a room be (x)m. Then,

Length = x + 50 % of x

= x + 50/100 × x

= x + x/2

= 2x + x/2

= 3x/2

Area of floor = 924/38.50

=> l × b = 924 × 100/3,850

=> x × 3x/2 = 24

=> 3x^2/2 = 24

=> x^2 = 24 × 2/3

=> x^2 = 16

=> x = √16

=> x = 4

Hence , breadth = 4m

length = 3 × 4/2

= 6m

Area of four walls = 1,320/5.50

=> 2(l+b) × h = 1,320 × 100/5.50

=> 2(6+4) × h = 240

=> 10h = 240/2

=> 10h = 120

=> h = 120/10

=> h = 12m

Hence , the dimensions of the room is 6m , 4m and 12m.

Thanks

Answer 2

Length of room=L
Breadth of room=B
Height of room=H
Since L is 50% more than breadth,
L=2B - - - - - - - - - (1)

Carpeting=₹924 @ ₹38.50/m²
Area of the room floor=924/38.50=23.75m²
L*B=23.75 - - - - - - - - - - - (2)
Put (1) in (2),
2B*B=23.75
2B²=23.75
B²=11.875
b = \sqrt{(11.875)}b=(11.875)​ 
B=3.446m
Hence L=2*3.446
L=6.892m


Painting the walls=₹1320 @ ₹5.50/m²
Area of four walls=1320/5.50=240m²
(L*H) + (B*H) + (L*H) + (B*H) = 240
2(L*H)+2(B*H)=240
2[(L*H)+(B*H)]=240
(L*H)+(B*H) =120
H(L+B)=120
H*(6.892+3.446)=120
H*10.338=120
H=120/10.338
H=11.608m

Hence dimensions of the room are
Length=L=6.892m
Breadth=B=3.446m
Height=H=11.608m