Question

The lenght of a room is 50./. More then its breadth The cost of carpaiting The room at The rate of rs38.50m2.is rs 924 and The cost of painting The walls at The rate of rs 5.50per m2 is equal to rs 1320 find The dimensions of The room?

Answer 1

Let the breadth, b=x.
length =(50% x) + x.
=(3/2)x.
Area of the floor = total cost of carpeting the floor ÷ cost per unit area
=924/38.5
=24m²
Area =l.b
=(3/2)x.x
=(3/2)x²
x²= 16
x=4m.

So breadth is 4m and length is 6m.

Let h be the height of room

• Now for painting the wall, if both the lateral area and top of the room are painted, then

area painted= total cost of painting÷ cost per unit area
= 1320/5.5
=240m²

Area = 2bh + 2lh +lb
240=2(4h+6h) +24
20h=216
h=10.8m


So dimensions of the room are 4m,6m,10.8m.

• if only lateral surface area is painted and top is not painted, then,

area =1320/5.5
=240m²
240=2bh +2lh
240=2(4h+6h)
240=20h
h=12m.

So the dimensions of the room are 4m,6m and 12m.