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- 11. If the length of a certain rectangle is decreased by 4 cm and the width is increased by 3 cm, a square with the same area as the original rectangle would result. Find the perimeter of the original rectangle.
A.40 cm
B.45 cm
C.50 cm
D.52 cm
Answer & Explanation
Answer: Option C 
Let x and y be the length and breadth of the rectangle respectively.
Then, x - 4 = y + 3 or x - y = 7 ----(1)
Area of the rectangle =xy; Area of the square = (x - 4) (y + 3)
(x - 4) (y + 3) =xy 3x - 4y = 12 ----(2)
Solving 1 & 2 , we get x = 16 and y = 9.
Perimeter of the rectangle = 2 (x + y) = [2 (16 + 9)] cm = 50 cm.
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- 12. A room is half as long again as it is broad. The cost of carpeting the at Rs. 5 per sq. m is Rs. 270 and the cost of papering the four walls at Rs. 10 per m2 is Rs. 1420. If a door and 2 windows occupy 8 sq. m, find the height of the room.
A.4 m
B.4.5 m
C.5 m
D.5.5 m
Answer & Explanation
Answer: Option C
Let breadth = x m, length = 3x m, height = H metres.
Area of the floor = (Total cost of carpeting)/(Rate/m2)=(270/5)m2=54m2.
x× (3x/2) = 54 =>x2 = (54×2/3) = 36 x = 6.
So, breadth = 6 m and length =(3/2)×6 = 9 m.
Now, papered area = (1420/10)m2 = 142 m2.
Area of 1 door and 2 windows = 8 m2.
Total area of 4 walls = (142 + 8) m2 = 150 m2
2×(9+ 6)× H = 150 H = 150/30 = 5 m.
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- 13. a ratio between the area of a square of side a and an equilateral triangle of side a is
A.2:√3
B.1:√3
C.√3:1
D.4:√3
Answer & Explanation
Answer: Option D
Area of square/area of triangle = a2/(√3/4)a2
= 4/√3 i.e 4:√3
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- 14. Length and Breadth of a rectangle is 7 m and 3.5 m respectively. Find the area of circle of maximum radius
A.9.625
B.9.74
C.9.8
D.9.725
Answer & Explanation
Answer: Option A
area of circle = πb2/4
= 22/7 × 3.52/4
= 9.625sq.m
View Answer
- 15. Find the area of a rhombus one side of which measures 20 cm and one diagonal is 24 cm.
A.370 cm2
B.365 cm2
C.380 cm2
D.384 cm2
Answer & Explanation
Answer: Option D
Since diagonals of a rhombus bisect each other at right angles, we have:
(20)2 = (12)2 + (x)2 =>x =√(20)2 – (12)2= √256= 16 cm. _I
So, other diagonal = 32 cm.
Area of rhombus = (1/2) x (Product of diagonals) =(1/2× 24 x 32) cm2 = 384 cm2
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