Question

The length and breadth of a rectangular room are in the ratio 3:2.if the length is 8m40cm find the area of the room.if the floor is to be covered with a carpet 1m 40cm wide.find the cost of the carpet at rs 25per metre

Answer 1

Let length of rectangular room be 3M and breadth be 2M.

Length of room is 8 m 40 cm (given in question)

So, length of room = 800 + 40 = 840 cm

But on the same side we have given length and breadth of the room are in the ratio 3:2.

So,

=> 3M = 840

=> M = 280

Length of room : 3M

=> 3(280)

=> 840 cm

=> 8.4 m

Breadth of room : 2M

=> 2(280)

=> 560 cm

=> 5.6 m

Area of rectangle = length × breadth

=> 8.4 × 5.6

=> 47.04 m²

Breadth of carpet = 1 m 40 cm

=> 100 + 40

=> 140 cm

=> 1.4 m

Area of carpet = Area of room

Area of carpet = length × breadth

=> 47.04 = length × 1.4

=> length = 33.6 cm

Cost of carpet at Rs. 25 per meter = 25 × 33.6

=> Rs. 840

Answer 2

Answer:

${\bold{\therefore Cost\:of\:carpet=840\:rupees}}$

Step-by-step explanation:

${\bold{\huge{\underline{SOLUTION-}}}}$

• In the given question information given about rectangular room whose length is given and length and breadth ratio is given.

• breadth of carpet is also given.

• So we have to find the cost to make the carpet for the floor.

$\underline \bold{Given: } \\ \implies Ratio \: of \: sides = 3 : 2 \\ \implies Length \: of \: room= 8.4 \: m \\ \implies Breadth \: of \: carpet = 1.4 \: m \\ \\ \underline \bold{To \: Find :} \\ \implies Cost \: of \: carpet \: to \: cover \: floor= ?$

• According to given question :

$\bold{ For \: length} \\ \implies Length = 3x \\ \implies 8.4\: m = 3x \\ \implies x = \frac{8.4}{3} \\ \bold{\implies x = 2.8 \: m} \\ \\ \bold{For \: breadth} \\ \implies Breadth = 2x = 2 \times 2.8\\ \bold{\implies Breadth = 5.6 \: m} \\ \\ \implies Area \: of \: rectangle \: floor = l \times b \\ \implies Area = 8.4 \times 5.6 \\ \bold{\implies Area = 47.04 \: {m}^{2} } \\ \\ \bold{Area \: of \: carpet = Area\:of\:room} \\ \implies l\times b=47.04\:m^{2} \\ \implies Length= \frac{47.04}{1.4} \\ \bold{\implies Length= 33.6 \: m }\\ \\ \bold{Cost \: of \: 1m \: carpet = 25 \: rupees} \\ \implies Cost \: of \: 33.6 \: m = 25 \times 33.6 \\ \bold{\implies Cost = 840 \: rupees} \\ \\ \bold{\therefore Cost \: of \: making \: carpet \: is \: 840 \: rupees}$