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Case Study I Ritesh bought a new well-furnished two-bedroom flat in a society. The layout of the flat is shown in the figure alongside. The builder claims that the areas of the two bedrooms and the kitchen together is 95 square metres. All the dimensions in the figure are in metre (m).

Ritesh bought a new well-furnished two-bedroom flat in a society. The layout of the flat is shown in the figure alongside. The builder claims that the areas of the two bedrooms and the kitchen together is 95 square metres. All the dimensions in the figure are in metre (m). R.S. Aggarwal Mathematics Solutions ICSE Class 9.

Study the above information and answer the following questions.

  1. Which of the following pair of linear equations represent the given situation?
    (a) x + y = 19, 2x + y = 13
    (b) x + y = 13, 2x + y = 19
    (c) x − y = 19, 2x − y = 13
    (d) x + y = 13, 2x − y = 19

  2. The perimeter of the outer boundary of the layout is:
    (a) 54 m
    (b) 27 m
    (c) 50 m
    (d) 52 m

  3. Total area of bedroom 1 and kitchen is:
    (a) 60 m2
    (b) 70 m2
    (c) 65 m2
    (d) 95 m2

  4. The area of the living room is:
    (a) 50 m2
    (b) 60 m2
    (c) 70 m2
    (d) 75 m2

  5. The cost of laying tiles on the floor of the kitchen at the rate of ₹200 per sq m is:
    (a) ₹ 7,000
    (b) ₹ 6,000
    (c) ₹ 5,200
    (d) ₹ 5,000

Linear Equations

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Answer

1. Given,

From picture,

x = Length of Bedroom 1, y = Length of kitchen

Length of bathroom = 2

Equations:

Length of rectangular flat = x + y + 2

In rectangle, opposites sides are equal.

⇒ x + y + 2 = 15

⇒ x + y = 15 - 2

⇒ x + y = 13     ….(1)

Area = length × breadth

From figure,

Area of each Bedroom = 5 × x

Area of Kitchen = 5 × y

Given,

Area of two bedrooms and kitchen is 95.

⇒ 2 × (5 × x) + 5 × y = 95

⇒ 10x + 5y = 95

⇒ 5(2x + y) = 95

⇒ 2x + y = 955\dfrac{95}{5}

⇒ 2x + y = 19

⇒ 2x + y = 19     ….(2)

Subtracting equation (1) from (2), we get :

⇒ 2x + y - (x + y) = 19 - 13

⇒ x = 6 m.

Substituting value of x in equation (1), we get :

⇒ 6 + y = 13

⇒ y = 13 - 6 = 7 m.

Hence, Option (b) is the correct option.

2. From figure,

⇒ Breadth = 15 m

⇒ Length = 5 + 2 + 5 = 12 m

Perimeter = 2(l + b)

= 2(12 + 15)

= 2 × 27

= 54 m.

Hence, Option (a) is the correct option.

3. Given,

Area of bedroom1 = l × b

= x × 5

= 6 × 5

= 30 m2.

Area of kitchen = l × b

= y × 5

= 7 × 5

= 35 m2.

Area of Bedroom 1 + Kitchen = 30 + 35 = 65 m2.

Hence, option (c) is the correct option.

4. From figure,

Area of bedroom 2 = l × b = 5 × x = 5 × 6 = 30 m2.

Area of bedroom2 + living room = l × b

= 15 × 7

= 105 m2.

Area of living room = 105 - area of bedroom2 = 105 - 30 = 75 m2.

Hence, option (d) is the correct option.

5. Given,

Area of kitchen = l × b

= y × 5

= 7 × 5

= 35 m2.

Cost of laying tiles on the floor of the kitchen at the rate of ₹ 200 per sq m = 35 × 200 = ₹ 7,000.

Hence, Option (a) is the correct option.

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