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6.
The length of a rectangular plot of land is three times as much as its breadth. A playground measuring 1200 sq. ft. occupies one-fourth of the total area of the plot. What is the length of the plot in feet?
  • A.
    40
  • C.
    120
  • B.
    360
  • D.
    Data inadequate.
  • Answer & Explanation
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Answer : [C]
Explanation :
Let the length and breath of the plot be 3x and x feet, respectively.
Total area of the plot = 4 x 1200 = 4800 sq ft.
 
 
  x + 3x = 4800
 
 
  x = 40 ft
 
 
  Length = 3 x 40 = 120 ft.
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7.
The length of each side of a triangle is 12 cm. The height of the triangle is
  • A.
    3 2  cm  
  • C.
    6 2  cm  
  • B.
    6 3  cm  
  • D.
    None of these
  • Answer & Explanation
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Answer : [B]
Explanation :
Each side = 12 cm
Then, S = 
12 + 12 + 12
2
 = 18    
Area =  18(18 - 12)(18-12)(18-12)        
18 x 6 x 6 x 6
=
1
2
 x 12 x height
     
or, height =
36 3
6
=
6 3 cm
     
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8.
If the sides of a rectangle are increased by 20% the percentage increase in its perimeter is
  • A.
    80
  • C.
    20
  • B.
    40
  • D.
    None of these
  • Answer & Explanation
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Answer : [C]
Explanation :
If length of the rectangle is L and its width is B, then its perimeter = 2(L + B)
Increased length = 1.2L,
Increased width = 1.2B
Increase perimeter = 2(1.2L  + 1.2B)
  = 2 x 1.2(L + B)  
  = 2.4(L + B)  
Increase in perimeter = 0.4(L + B)
Percentage increase =
0.4(L + B)
2(L + B)
 x 100 = 20%  
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9.
The perimeter of an isosceles triangle is 306 m and each of the equal sides is
5
8
 of the base.
Find the area.
  • A.
    3648 cm
  • C.
    3846 cm
  • B.
    3468 Sq. m
  • D.
    None of these
  • Answer & Explanation
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Answer : [B]
Explanation :
Given: a
5
8
 b    
Now, perimeter of isosceles triangle = 2a + b
 
  306 = 2 x
5
8
 b + b or, b = 136        
 
  a
5
8
 b =
5
8
 x 136 = 85
 
  Area is isosceles triangle = 
b
4
 
4a2 - b2
 
Area is isosceles triangle = 
136
4
 
4 x (85)2 - (136)2
 
34 x 102 = 3,468 m2  
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10.
A man runs a circle of 50 m radius at a speed of 12 km per hour. Find the time taken by him for going around it ten times.
  • A.
    10 min
  • C.
    15.7 min
  • B.
    12.5 min
  • D.
    None of these
  • Answer & Explanation
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Answer : [C]
Explanation :
Distance = 2 x 3.14 x 50 x 10 = 3140 m
12 km/hr =
10
3
 m/sec  
Time = 
3140
10/3
 = 942 sec  
942
60
 = min  
  = 15.7 min
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