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
Rubrics to be kept in mind while answering :
➡ Answer should be explained Step-by-Step with sections of 'Given', 'To Find' and 'Solution'.
➡ Content Quality needed.
➡ No Spam and Copied Answers!
If the given rubrics are followed, then answer will be marked as Brainliest!
But if the rubrics are not followed, then it will be reported on the spot!
Answers
Answer:
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 metre allowing an area of 15 sq. m for doors and windows. The height of the room is: (a) 2.6m (b) 3.9m (c) 4m (d) 4.2m (e) None of these area and volumeRead more on Sarthaks.com - https://www.sarthaks.com/54343/the-ratio-height-room-its-semi-perimeter-costs-260-paper-the-walls-of-the-room-with-paper-50
Answer:
option (c) 4 m
Step-by-step explanation:
Given :
- 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.
To find :
the height of room
Solution :
Let the length, breadth and height of the room be l, b and h respectively.
Semi perimeter of the room = (l + b)
Let
the height, h= 2x
then, semi perimeter = 5x
l + b = 5x
Area of 4 walls of the room = lh + bh + lh + bh
= h(l + b + l + b)
= h(2l + 2b)
= 2(l + b) × h
= 2(5x) (2x)
= 20x²
It's also given that the area occupied by doors and windows is 15 m²
so, area to be papered = (20x² – 15) m²
Breadth of the paper = 50 cm = 50/100 m = 0.5 m
Area to be papered = Area of the paper
20x² – 15 = length × 0.5
length = 2(20x² – 15)
length = 40x² – 30
It costs Rs. 260 to paper the walls of the room with paper 50 cm wide at Rs. 2 per meter
2 × (40x² – 30) = 260
80x² – 60 = 260
80x² = 260 + 60
80x² = 320
x² = 320/80
x² = 4
x = √4
x = 2
Height of the room = 2(2) = 4 m