Question

The height of a room is 40% of its semi - perimeter. It costs 260 rupees to paper the walls of the room with paper 50 cm wide at 2 rupees per metre allowing an area of 15 m^2 for doors and windows. The height of the room is ?​ Plz don't copy.​

Answer 1

Answer:

$\huge\underline\bold {Answer:}$

Let the length, breadth and height of the room be l, b and h respectively. Then, h = 0.4(l + b)

Area of four walls = 2(l + b)h

= 2(l + b) × 0.4(l + b)

= 0.8(l + b)^2

Therefore area which is prepared

= 0.8(l + b)^2 – 15

Now, area of paper = Area of wall

=> Length × breadth

= 0.8(l + b)^2 – 15

=> Length

$= \frac{0.8(l + b) {}^{2} - 15 }{0.5} \: \: since \: \: width \: \: = \: \: 50 \: \: cm \\ = 0.5m$

Given,

$\frac{{0.8(l + b) {}^{2} - 15} }{0.5} \times 2 = 260$

$= > 0.8(l + b) {}^{2} - 15 = \frac{260 \times 0.5}{2} \\ = > 0.8(l + b) {}^{2} - 15 = 65 \\ = > 0.8(l + b) {}^{2} = 65 + 15 = 80 \\ = > (l + b) {}^{2} = \frac{80}{0.8} = 100 \\ = > l + b = 10$

Therefore h = 0.4 × 10 = 4 m.

Answer 2

Answer:

4 meter

Step-by-step explanation:

_______________________________

To find :—

The height of the room .

Formula applied :—

• 2 ( l + b ) h
• Length × breath

Solution :—

We have to write length as l , breath as b and height as h .

here,

h = 0.4 ( l + b )

Now,

Area of the 4 walls = 2 ( l + b ) h

= 2 ( l + b ) × 0.4 ( l + b )

= 0.8 ( l + b ) ²

Therefore, area that prepared = 0.8 ( l + b ) ² – 15

So now,

Area of paper = Area of the wall

= Length × breath

= 》 length =0.8 ( l + b ) ² – 15

$length = \frac{0.8(l + {b)}^{2} }{0.5} - 15$

Then,

$since \: 50 \: cm = \frac{50}{100}$

$= 0.5 \: m$

Here given ,

$\frac{0.8(l + {b}^{2} ) - 15 }{0.5} \times 2 = 260$

$0.8(l + b {)}^{2} - 15 = \frac{260 \times 0.5}{2}$

$0.8(l + b {)}^{2} - 15 = 65$

$0.8(l + b {)}^{2} = 65 + 15 = 80$

$(l + b {)}^{2} = \frac{80}{0.8} = 100$

$l + b = 10$

Therefore , h = 0.4 × 10 = 4 m