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11.
If the height of an equilateral triangle is 2 3  cm, then the length of its side is    
  • A.
    4 cm
  • C.
    5 cm
  • B.
    6 cm
  • D.
    None of these
  • Answer & Explanation
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Answer : [A]
Explanation :
Height of the equilatereral triangle =
3
2
 x (side)    
 
 
 
2 3  
=
3
2
 x (side)    
 
  Side of the equilateral triangle = 4 cm  
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12.
If a diagonal of a square is doubled, how does the area of the square change?
  • A.
    Becomes four-fold
  • C.
    Becomes two-fold
  • B.
    Becomes three-fold
  • D.
    None of these
  • Answer & Explanation
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Answer : [A]
Explanation :
Let originally, diagonal = x
 
 
 Original area =
1
2
 x2    
After increase, diagonal = 2x
New area = 
1
2
 (2x)2
     
 
 
 
Original area
New area
=
1
4
     
 
 
  New area = 4 (original area)  
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13.
If the base of a parallelogram is (x + 4), altitude to the base is (x - 3) and the are is (x2 - 4), then the actual area is equal to
  • A.
    4 sq units
  • C.
    60 sq units
  • B.
    48 sq units
  • D.
    None of these
  • Answer & Explanation
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Answer : [C]
Explanation :
Area of the parallelogram = base x altitude
 
 
  (x - 4) = (x - 4) x (x - 3)
 
 
  x2 - 4 = x2 + 4x - 3x - 12
 
 
  x = 8
 
 
  Area of the parallelogram = x2 - 4 = (8)2 - 4 = 60 square units
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14.
If  area of a triangle whose base is 6 cm is equal to the area of a circle of radius 6 cm, find the height of this triangle
  • A.
    10 cm
  • C.
    12 cm
  • B.
    22 cm
  • D.
    18 cm
  • Answer & Explanation
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Answer : [C]
Explanation :
Radius of the circle = 6 cm
Area of the circle = 36 sq m
According to question:
Area of the triangle of base 6 cm = Area of the circle of radius 6 cm
 
 
 
1
2
 x base x height = 36    
 
 
 
1
2
 x 6 x height = 36    
 
 
  Height of the triangle =
36 x 2
6
 = 12 cm.    
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15.
A plot of land is in the shape of a right-angled isosceles triangle. The length of hypotenuse
is 50 2  m. The cost of fencing is Rs. 3 per metre. The cost of fencing the plot will be
  • A.
    Less than Rs. 300
  • C.
    more than Rs. 500
  • B.
    less than Rs. 500
  • D.
    None of these
  • Answer & Explanation
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Answer : [C]
Explanation :
Let the length of each of equal sides of the triangle be x m.
Then, x2 + x2 = (50 2 )2 = 5000    
 
  2x2 = 5000  
 
  x = 50  
 
  Perimeter of the triangle = 50 + 50 + 50 2  
  = 100 + 50 x 1.4146 = 170.73 m  
 
  Cost of fencing = Rs(170.73 x 3) = Rs 512.19  
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