.In the below given layout, the design and measurements has been made such that area of two bedrooms and Kitchen together is 95 sq. m.Based on the above information, answer the following questions:(Attempt any four)(i)Form the pair of linear equations in two variables from this situation.(ii)Find the length of the outer boundary of the layout.(iii)Find the area of each bedroom and kitchen in the layout.(iv)Find the area of living room in the layout.(v)Find the cost of laying tiles in Kitchen at the rate of Rs. 50 per sq. m
Answers
Given : area of two bedrooms and Kitchen together is 95 sq. m.
To Find :
(i)Form the pair of linear equations in two variables from this situation.(ii)Find the length of the outer boundary of the layout.
(iii)Find the area of each bedroom and kitchen in the layout.
(iv)Find the area of living room in the layout.
(v)Find the cost of laying tiles in Kitchen at the rate of Rs. 50 per sq. m
Solution:
Area of Bedroom1 = 5x
Area of bedroom 2 = 5x
Area of Kitchen = 5y
area of two bedrooms and Kitchen together is 95 sq. m
=> 5x + 5x + 5y = 95
=> 2x + y = 19
x + 2 +y = 15
=> x + y = 13
2x + y = 19
x + y = 13
=> x = 6 , y = 7
the length of the outer boundary of the layout = 2(( 5 + 2 + 5) + 15)
= 2(27)
= 54 m
.(iii) the area of each bedroom = 5x = 5(6) = 30 m²
area of kitchen = 5y = 5(7) = 35 m²
area of living room in the layout.
= Total area - area of 2 bedrooms - area of kitchen - area of bathroom
= 15 * 12 - 2(30) - 35 - 2*5
= 180 - 60 - 35 - 10
= 75 m²
cost of laying tiles in Kitchen at the rate of Rs. 50 per sq. m = 35 * 50
= 1750 Rs
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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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