Question

Heya! Answer the following Mathematical MCQ!

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 wide at Rs. 2 per meter allowing an area of 15 m² for door and windows. The height of room is :
a. 2.6 m
b. 3.9 m
c. 4 m
d. 4.2 m

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Answer 1

Let h = 2x metres and (l + b) = 5x metres.

Length of the paper

Total cost /Rate per m =260 /2

Area of the paper

{50/100} ×130 m² = 65 m².

Total area of 4 walls

= (65 + 15) m² = 80 m2.

.: 2(l+ b) x h = 80 m²

= 2*5x*2x = 80

= x² = 4

x= 2.

Height of the room = 4 m.

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