Question

4. 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.​

Answer 1

Solution :-

→ Area of 2 bedrooms + kitchen = 95 m²

→ 2(5 * x) + (5 * y) = 95

→ 10x + 5y = 95

→ 5(2x + y) = 95

→ 2x + y = 19 ----------- Eqn.(1)

also,

→ x + 2 + y = 15

→ x + y = 15 - 2

→ x + y = 13 ---------- Eqn.(2)

therefore, (a) 2x + y = 19 and x + y = 13 pair of linear equations does describe this situation . (Ans.i)

now,

→ Outer boundary of layout = 2(L + B) = 2(15 + 12) = 2 * 27 = 54 m (d) . (Ans.ii)

and, solving Eqn.(1) and Eqn.(2)

→ 2(x + y) - (2x + y) = 2 * 13 - 19

→ 2x + 2y - 2x - y = 26 - 19

→ y = 7

putting value of y in Eqn.(2)

→ x + 7 = 13

→ x = 13 - 7

→ x = 6 .

then,

→ Area of Bedroom 1 = L * B = x * 5 = 6 * 5 = 30m² (b) . (Ans.iii)

therefore ,

→ Area of Living room = 7(2 + y) + x * 2 = 7(2 + 7) + 6 * 2 = 7 * 9 + 12 = 63 + 12 = 75 m². (c) (Ans.iv) .

hence,

→ cost of laying tiles in kitchen = Rate / m² * Area of kitchen = 50 * (5 * y) = 250 * 7 = Rs.1750 . (c) (Ans.v)

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