Question

the ratio of Length breadth of a big room is 5:3:2 and its surface area is 1550cm find the dimensions of the room also find the cost of white washing the four walls and ceiling of the room at the rate of 6.95per mitre

Answer 1

Let,

Length of room = 5x
Breadth of room = 3x
Height of room = 2x

Now,

Surface area of Cuboidal room = 1550 cm^2

=> 2(lb+bh+hl) = 1550 cm^2

$= > 2(5x \times 3x + 3x \times 2x + 2x \times 5x) = 1550$

$= > 2(15 {x}^{2} + 6 {x}^{2} + 10 {x}^{2} ) = 1550$

$= > 31 \: {x}^{2} = 1550$

$= > {x}^{2} \: = \frac{1550}{31} \: = 50$
$= > x \: = \sqrt{50} = 7.07$
Now,
Length = 5x = 5 x 7. 07 = 35.35 cm
Breadth = 3x = 3 x 7.07 = 21.21 cm
Height = 2 x = 2 x 7. 07 = 14.14 cm

Now,

Area of 4 walls and ceiling = 2(l+b) x h + l xb

=> Area = 2(35.35+21.21) x 14.14 + 35.35 x 21.21

=> Area = 2(56.56) x 14.14 + 750

=> Area = (113.12 x 14.14 + 750) cm^2

=> Area = 1600+750 cm^2

=> Area = 2350 cm^2

Rate of Washing = Rs 6.95

Therefore,

Cost of Washing 2350 cm^2 = Rs [2350 x 6.95]

=> Cost = Rs 16332.5


Be Brainly

Answer 2

$\mathfrak {\underline{solution}}$

the measurements of room given in the ratio form like 5 :3:2.

let the ratio be x.

length (l) = 5x

breadth (b) = 3x

height (h) = 2x

here given ,

surface area of room = 1550cm^2

using formula here ,

surface area of room = 2 ( lb + bh + hl )

then,

2 ( lb + bh + hl ) = 1550cm^2

2 ( 5x * 3x + 3x * 2x + 2x * 5x ) = 1550cm^2

2 ( 15x + 6x + 10x ) = 1550cm^2

2 ( 31x) = 1550cm^2

31x^2 = 1550cm^2

x^2 = 1550 / 31

x^2 = 50 cm^2

x = √ 50

x = 7.07 cm

now put the values of x in ratio.

length (l) = 5x = 5 × 7.07 = 35.35cm

breadth (b) = 3x = 3 ×7.07=21.21cm

height (h) = 2x = 2 × 7.07 = 14.14cm

area of the rooms = 2 ( l + b) × h + l ×b

= 2 ( l + b) × h + l ×b

= 2 ( 35.35 + 21.21) * 14.14 + 35.35 ×14.14cm^2

= 2 ( 56.56 ) * 14.14 + 750cm^2

= 113.12 * 14.14 + 750 cm^2

= 1600 + 750cm^2

= 2350 cm^2

total area of room = 2350cm^2

rate of 1 metres washing room = 6.95.

so,

1 m^2 washing cost 6.95

then,

2350cm^2 cost = 2350 × 6.95

total cost = 16332.5 rs

be brainly