Q) Architect : An architect is a skilled professional who plans and designs buildings and generally plays a key role in their construction. Architects are highly trained in the art and science of building design. Since they bear responsibility for the safety of their buildings’ occupants, architects must be professionally licensed.

Varsha is a licensed architect and design very innovative house. She has made a house layout for her client which is given below. In the layout, the design and measurements has been made such that area of two bedrooms and kitchen together is 95 sq. m.​

(i) Which pair of linear equations does describe this situation?
(ii) What is the length of the outer boundary of the layout.
(iii) What is the area of bedroom 1 ? What is the area of living room in the layout?
(iv) What is the cost of laying tiles in Kitchen at the rate of Rs. 50 per sq. m ?

Ans:

STEP BY STEP SOLUTION

(i) Pair of Linear equations:

From the given rectangular layout in the diagram, opposite sides must be equal,

∴ X + 2 + Y = 15

∴ X + Y = 15 – 2

∴ X + Y = 13 ………….. (i)

Next, we are given a condition that the area of 2 bedrooms and kitchen together is 95 m²

From the diagram, area of a bedroom is 5 x X = 5 X m²

∴ Area of 2 bedrooms = 2 (5 X) = 10 X m²

Area of kitchen = 5 x Y = 5 Y m²

∴ Area of 2 bedrooms and kitchen together = (10 X + 5 Y) m²

Since this has to be equal to 95 m²

∴ 10 X + 5 Y = 95

∴ 2 X + Y = 19 …………. (ii)

Therefore, the pair of linear equations is: X + Y = 13 and 2 X + Y = 19

(ii) Length of the outer boundary of layout:

To find the outer boundary, we need to calculate the circumference of the layout

Since the circumference of a rectangle is given by 2 ( L + B)

The length of the given layout = 15 m

The breadth of the given layout = 5 + 2 + 5 = 12 m

∴ The boundary length of the given layout = 2 (15 + 12) = 54 m

Therefore, the length of the outer boundary is 54 m.

(iii) Areas of Bedroom 1 and Living room:

Step 1: To calculate the areas of bedroom 1 and the living room, we need to find values of X and Y

To find values of X and Y, let’s solve the pair of linear equations:

X + Y = 13 ………….. (i)

2 X + Y = 19 …………. (ii)

Step 2: By subtracting equation (i) from (ii), we get:

(2 X + Y) – (X + Y) = 19 – 13

∴ 2 X + Y – X – Y = 6

∴ X = 6

Step 3: By substituting the value of X in equation (i), we get:

(6) + Y = 13

∴ Y = 13 – 6

∴ Y = 7

Step 4: Area of bedroom 1 = 5 X

= 5 (6) = 30 m²

Step 5: Area of living room = 15 x (5 + 2) – Bedroom Area

= 15 x 7 – 30

= 105 – 30 = 75 m²

Therefore, the area of Bedroom 1 is 30 m² and area of Living room is 75 m²

(iv) Cost of laying tiles in Kitchen:

To calculate the cost of tile laying, first we need to calculate the area of the kitchen floor

Area of Kitchen = 5 Y =  5 (7) = 35 m²

Next, Cost of tile laying = Area of Kitchen x cost per m²

= 35 x 50 = 1750

 Therefore, the Cost of laying tiles in Kitchen is Rs. 1,750

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