Question

The ratio of height of a room to its semi-perimeter is 2 : 5. It costs Rs. 260 to paper the walls of the room with paper 50 cm

Answer 1

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Answer 2

Answer:

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