Question

The dimensions of the floor of a room and a carpet laid on the room of Arun's house is given in the picture. The room is in square shape and carpet is rectangular.

4p+6 ,4p+6,4p+6,4p+6 Floor

6p+9,2p+5 carpet

Find the area of the carpet​

Answer 1

Answer:

144 sq. unit

Step-by-step explanation:

It is given that,

Room in square shape and the carpet is of rectangular shape

but, area of room = area of carpet

∴ side² = l x b

∴ (4p +6)² = (6p + 9) x (2p + 5)

∴ (4p)² + 2 x 4p x 6 + 6² = 12p² + 30p + 18p + 45

∴ 16p² + 48p + 36 = 12p² + 48p + 45

∴ 16p² - 12p² = 45 - 36

∴ 4p² = 9

∴ p² = 9/4

∴ p = √9/4

∴ p = ± 3/2

Now, put the value of p in the area of carpet

we have,

Area of carpet = l x b

                     A = (6p + 9) x (2p + 5)

                 ∴  A = (6 x 3/2 + 9) x (2 x 3/2 + 5)

                 ∴ A = (3 x 3 + 9) x (3 + 5)

                 ∴ A = 18 x 8

                 ∴ A = 144

∴ Area of the carpet required = 144 sq. unit