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In the below given layout, the design and measurements has been made that area of two bedrooms and kitchen together is 95 sq.m.
The area of two bedrooms and kitchen are respectively equal to:
(i) 5x, 5y (ii) 10x , 5y (iii) 5x ,10y (iv) x , y
Find the length of the outer boundary of the layout.
(i) 27 m (ii) 15 m (iii) 50 m (iv) 54 m
The pair of linear equation in two variables formed from the statements are
(i) x + y = 13, x + y = 9
(ii) 2x + y = 13 , x + y =9
(iii) x + y = 13 , 2x+ y =9
(iv) none of these
Which is the solution satisfying both the equations formed in (iii)….
(a) x =7, y =6
(b) x =8 , y =5
(c) x =6, y =7
(d) X =5 , y =8
Find the area of each bedroom?
Answers
Given :- 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 layout and situation, answer the following questions :
(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 :-
given that,
→ Length of bedroom = x m.
→ Breadth of bedroom = 5 m.
So,
→ Area of bedroom = Length * breadth = x * 5 = 5x m².
Than,
→ Area of 2 bedrooms = 2 * 5x = 10x m².
Now,
→ Length of kitchen = y m.
→ Breadth of kitchen = 5 m.
So,
→ Area of kitchen = Length * breadth = y * 5 = 5y m².
Now, we have given that,
→ Area of 2 bedrooms + Area of kitchen = 95 m².
→ 10x + 5y = 95 ------------ Eqn.(1)
and,
→ x + 2 + y = 15
→ x + y = 15 - 2
→ x + y = 13 --------------- Eqn.(2) .
{ Required pair of linear equations in two variables. Answer of (i) .}
Now, Multiply Eqn.(2) by 5 and subtraction from Eqn.(1) , we get,
→ (10x + 5y) - 5(x + y) = 95 - 5*13
→ 10x - 5x + 5y - 5y = 95 - 65
→ 5x = 30
dividing both sides by 5,
→ x = 6.
Putting value of x in Eqn.(2) ,
→ 6 + y = 13
→ y = 13 - 6
→ y = 7.
Therefore,
→ Area of kitchen = 5y = 5 * 7 = 35 m² (Ans. iii)
→ Area of each bedroom = 5 * 6 = 30 m² (Ans. iii) .
hence,
→ Answer (ii) = 12 m and 15m.
→ Answer (iv) = Area of living room = (15 * 7) - Area of bedroom 2 = 105 - 30 = 75 m² (Ans.)
→ Answer (v) = The cost of laying tiles in Kitchen at the rate of Rs. 50/m² = Area of kitchen * 50 = 35 * 50 = Rs.1750 (Ans.)
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