91. A piece of wire 132 cm. long is bent successively in the shape of an equilateral triangle, a square and a circle. Then area will be longest in shape of
    

1. 1. Circle
      

   
   
   

   2. Equilateral triangle
      

   
   
   

   3. Square
      

   
   
   

   4. Equal in all the shapes

   
   
   

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1. View Hint View Answer Discuss in Forum

   Side of equilateral triangle =	132	= 44 cm.
   	3

   
   Its area =
   

   =		√3	× 44 × 44		sq. cm
   		4

   
   = 484√3 sq. cm.
   = 484 × 1.7 = 822.8 sq. cm.
   Side of square = 132/4 = 33 cm.
   Area of square = 33 × 33 = 1089 sq. cm.
   Circumference of circle = 2πr
   

   ⇒ 2 ×	22	×r = 132
   	7

   
   

   ⇒ r =	132 × 7	= 21 cm.
   	2 × 22

   
   

   ∴ area of circle =	22	× 21 × 21 = 1386 sq.cm.
   	7

   Correct Option: A

   Side of equilateral triangle =	132	= 44 cm.
   	3

   
   Its area =
   

   =		√3	× 44 × 44		sq. cm
   		4

   
   = 484√3 sq. cm.
   = 484 × 1.7 = 822.8 sq. cm.
   Side of square = 132/4 = 33 cm.
   Area of square = 33 × 33 = 1089 sq. cm.
   Circumference of circle = 2πr
   

   ⇒ 2 ×	22	×r = 132
   	7

   
   

   ⇒ r =	132 × 7	= 21 cm.
   	2 × 22

   
   

   ∴ area of circle =	22	× 21 × 21 = 1386 sq.cm.
   	7

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92. Let ∆ABC and ∆ABD be on the same base AB and between the same parallels AB and CD. Then the relation between areas of triangles ABC and ABD will be

1. 1. ∆ABD =	1	∆ ABC
      	3

   
   
   

   2. ∆ABD =	1	∆ ABC
      	2

   
   
   

   3. ∆ABC =	1	∆ ABD
      	2

   
   
   

   4. ∆ABC = ∆ABD

   
   
   

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1. View Hint View Answer Discuss in Forum

   The areas of triangles on the same base and between the same parallel lines are equal.
   ∴ ∆ABC = ∆ABD
   298. (2) Perimeter of rhombus
   = 4 × side
   

   ∴ Each side =	240	= 60 metre
   	4

   
   Distance between parallel sides = 20 metre
   ∴ Area of rhombus = 60 × 20 = 1200 sq. metre

   Correct Option: D

   The areas of triangles on the same base and between the same parallel lines are equal.
   ∴ ∆ABC = ∆ABD
   298. (2) Perimeter of rhombus
   = 4 × side
   

   ∴ Each side =	240	= 60 metre
   	4

   
   Distance between parallel sides = 20 metre
   ∴ Area of rhombus = 60 × 20 = 1200 sq. metre

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93. The perimeter of a rhombus is 240 metre and the distance between any two parallel sides is 20 metre. The area of the rhombus in square metre is
    

1. 1. 600 square metre
      

   
   
   

   2. 1200 square metre
      

   
   
   

   3. 2400 square metre
      

   
   
   

   4. 4800 square metre

   
   
   

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1. View Hint View Answer Discuss in Forum

   Perimeter of rhombus = 4 × side
   

   ∴ Each Side =	240	= 60 metre
   	4

   
   Distance between parallel sides = 20 metre
   ∴ Area of rhombus = 60 × 20
   = 1200 sq. metre

   Correct Option: B

   Perimeter of rhombus = 4 × side
   

   ∴ Each Side =	240	= 60 metre
   	4

   
   Distance between parallel sides = 20 metre
   ∴ Area of rhombus = 60 × 20
   = 1200 sq. metre

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94. The area of the largest triangle that can be inscribed in a semicircle of radius 6 m is
    

1. 1. 36 m²
      

   
   
   

   2. 72 m²
      

   
   
   

   3. 18 m²
      

   
   
   

   4. 12 m²

   
   
   

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1. View Hint View Answer Discuss in Forum

   
   The angle in a semi-circle is a right angle.
   Let point C be the mid-point of arc ABC.
   Maximum height of ∆ABC = OC = radius
   

   ∴ Area of triangle ABC =	1	× AB × OC
   	2

   
   

   =	1	× 12 × 6 = 36sq. metre
   	2

   Correct Option: A

   
   The angle in a semi-circle is a right angle.
   Let point C be the mid-point of arc ABC.
   Maximum height of ∆ABC = OC = radius
   

   ∴ Area of triangle ABC =	1	× AB × OC
   	2

   
   

   =	1	× 12 × 6 = 36sq. metre
   	2

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95. A circle and a square have same area. The ratio of the side of the square to the radius of the circle will be:
    

1. 1. √π : 1
      

   
   
   

   2. 1 : √π
      

   
   
   

   3. π² : 1
      

   
   
   

   4. 1 : π

   
   
   

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1. View Hint View Answer Discuss in Forum

   Area of circle = πr²
   Area of square = side²
   ∴ Side² = πr²
   

   ⇒	Side²	= π
   	r²

   
   

   ∴	Side	= √π - 1
   	r

   Correct Option: A

   Area of circle = πr²
   Area of square = side²
   ∴ Side² = πr²
   

   ⇒	Side²	= π
   	r²

   
   

   ∴	Side	= √π - 1
   	r

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