Amit is planning to buy a house and the layout is given below. The design and the measurement has been made such that areas of two bedrooms and kitchen together is 95 sq. m.

Based on the above information, answer the following questions:

Question 1

Form the pair of linear equations in two variables from this situation.

Question 2

Find the length of the outer boundary of the layout.

Question 3

Find the area of each bedroom and kitchen in the layout.

Question 4

Find the area of living room in the layout.

Question 5

Find the cost of laying tiles in kitchen at the rate of Rs. 50 per sq.m

Question Amit is planning to buy a house and the layout is given below. The design and the measurement has been made such that areas of two bedrooms and kitchen together is 95 sq. m. Question 1 Form the pair of linear equations in two variables from this situation.
Given
Length = 15 m
x + 2 + y = 15
x + y = 13
Also, given that
Area of two bedrooms + Kitchen = 95 square meter
2(5 × x) + 5 × y = 95
10x + 5y = 95
Dividing both sides by 5
2x + y = 19
Question 2 Find the length of the outer boundary of the layout.
Length of outer boundary of layout
= Perimeter of Rectangle
= 2 × (Length + Breadth)
= 2 × (12 + 15)
= 2 × 27
= 54 m
Question 3 Find the area of each bedroom and kitchen in the layout.
To find Area, we need to find x and y
Solving equations (1) and (2)
x + y = 13 …(1)
2x + y = 19 …(2)
From (1)
x + y = 13
y = 13 − x
Putting value of y in (2)
2x+ y = 19
2x + (13 − x) = 19
2x − x = 19 − 13
x = 6
Putting x = 6 in (1)
y = 13 − x
y = 13 − 6
y = 7
Thus, x = 6 m and y = 7 m
Now,
Area of bedroom = 5 × x = 5 × 6 = 30 m2
Area of kitchen = 5 × y = 5 × y = 35 m2
Question 4 Find the area of living room in the layout.
Area of living room
= Area of 15 × 7 rectangle − Area of bedroom
= (15 × 7) – 30
= 105 – 30
= 75 m2
Question 5 Find the cost of laying tiles in kitchen at the rate of Rs. 50 per sq.m
Area of kitchen = 35 m2
Given that
Cost of laying 1 m2 tiles in the kitchen = Rs. 50
Cost of laying 35 m2 tiles in the kitchen = Rs 50 × 35
= Rs 1750

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 10 years. He provides courses for Maths and Science at Teachoo.