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16.
The sides of a triangle are in the ratio 3 : 4 : 5. If its perimeter is 36 cm, area of the triangle is
  • A.
    57 sq m
  • C.
    56.5 sq m
  • B.
    54 sq m
  • D.
    None of these
  • Answer & Explanation
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Answer : [B]
Explanation :
The sides of the triangle are
a = 
3
12
 x 36 = 9cm, b =
4
12
 x 36 = 12 cm
c = 
5
12
 x 36 = 15 cm      
s = 
a + b + c
2
 x 36 = 15 cm      
 
 
 Area =  s(s-a)(s-b)(s-c)        
18(18-9)(18-12)(18-15)    
18 x 9 x 6 x 3    
92 x 22 x 32    
9 x 2 x 3    
54 sq cm.    
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17.
A field is in the shape of a parallelogram. Its adjacent sides and one diagonal are 65 m, 119 m and 156 m, respectively. Find the cost of gravelling it at the rate of Rs. 10 per sq m.
  • A.
    Rs. 81400
  • C.
    Rs. 91400
  • B.
    Rs. 71400
  • D.
    None of these
  • Answer & Explanation
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Answer : [B]
Explanation :
We have, s = 
a + b + d
2
 = 18    
65 + 119 + 156
2
 = 170    
 
 
  Area of parallelogram  
2 s(s - a)(s - b)(s - d)        
2 170(170 - 65)(170 - 119)(170 - 156)        
2 170 x 51 x 105 x 14        
2 x 3570      
7140 m2      
 
 
  Cost of gravelling = 7140 x 10 = Rs 71,400  
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18.
The radius of the wheel of a vehicle is 70 cm. The wheel makes 10 revolutions in 5 seconds. The speed of the vehicle is
  • A.
    29.46 km/hr
  • C.
    36.25 km/hr
  • B.
    31.68 km/hr
  • D.
    32.72 km/hr
  • Answer & Explanation
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Answer : [B]
Explanation :
Circumference =   2 x
22
7
 x 70    cm = 440 cm  
Distance traveled in 10 revolutions = 4400 cm = 44 m
 
 
  Speed =
Distance
Time
=  
44
5
   m/sec  
   
44
5
x
18
5
   km/hr = 31.68 km/hr  
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