571. One side of a square is increased by 30%. To maintain the same area, the other side will have to be decreased by
     

1. 1. 23	1	%
      	13

      
      

   
   
   

   2. 76	12	%
      	13

      
      

   
   
   

   3. 30%
      

   
   
   

   4. 15%

   
   
   

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1. View Hint View Answer Discuss in Forum

   Using Rule 10,
   If the required percentage be x, then
   

   30 - x -	30x	= 0
   	100

   
   ⇒ 300 – 10x – 3x = 0
   

   	Percentage Effect =		x + y +	xy		%
   				100

   
   ⇒ 13x = 300
   

   ⇒ x =	300	= 23	1	%
   	13		13

   Correct Option: A

   Using Rule 10,
   If the required percentage be x, then
   

   30 - x -	30x	= 0
   	100

   
   ⇒ 300 – 10x – 3x = 0
   

   	Percentage Effect =		x + y +	xy		%
   				100

   
   ⇒ 13x = 300
   

   ⇒ x =	300	= 23	1	%
   	13		13

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572. The length and breadth of a rectangle are doubled. Percentage increase in area is
     

1. 1. 150%
      

   
   
   

   2. 200%
      

   
   
   

   3. 300%
      

   
   
   

   4. 400%

   
   
   

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1. View Hint View Answer Discuss in Forum

   Using Rule 10,
   

   Percentage increase in area =		100 + 100 +	100 × 100		% = 300%
   			100

   Correct Option: C

   Using Rule 10,
   

   Percentage increase in area =		100 + 100 +	100 × 100		% = 300%
   			100

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573. If the area of a triangle with base 12 cm is equal to the area of a square with side 12 cm, the altitude of the triangle will be
     

1. 1. 12 cm
      

   
   
   

   2. 24 cm
      

   
   
   

   3. 18 cm
      

   
   
   

   4. 36 cm

   
   
   

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1. View Hint View Answer Discuss in Forum

   Using Rule 1 and 10,
   Area of square = (12)² = 144 cm²
   

   Area of triangle =	1	× base × height
   	2

   
   

   =	1	× 12 × height
   	2

   
   

   ⇒	1	× 12 × height = 144
   	2

   
   

   ⇒ Height =	144 × 2	= 24cm.
   	12

   Correct Option: B

   Using Rule 1 and 10,
   Area of square = (12)² = 144 cm²
   

   Area of triangle =	1	× base × height
   	2

   
   

   =	1	× 12 × height
   	2

   
   

   ⇒	1	× 12 × height = 144
   	2

   
   

   ⇒ Height =	144 × 2	= 24cm.
   	12

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574. The ratio of the areas of the circumcircle and the incircle of an equilateral triangle is
     

1. 1. 2 : 1
      

   
   
   

   2. 4 : 1
      

   
   
   

   3. 8 : 1
      

   
   
   

   4. 3 : 2

   
   
   

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1. View Hint View Answer Discuss in Forum

   For the equilateral triangle of side a,
   

   In radius =	a
   	2√3

   
   

   Circum-radius =	a
   	√3

   
   

   ∴ Required ratio =		a		²	: π		a		²
   		√3					2√3

   
   

   =	1	:	1	= 4 : 1
   	3		12

   Correct Option: B

   For the equilateral triangle of side a,
   

   In radius =	a
   	2√3

   
   

   Circum-radius =	a
   	√3

   
   

   ∴ Required ratio =		a		²	: π		a		²
   		√3					2√3

   
   

   =	1	:	1	= 4 : 1
   	3		12

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575. Area of the incircle of an equilateral triangle with side 6 cm is

1. 1. π	sq. cm
      2

   
   
   

   2. √3π sq. cm.
      

   
   
   

   3. 6π sq. cm.
      

   
   
   

   4. 3π sq. cm.

   
   
   

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1. View Hint View Answer Discuss in Forum

   
   DB = DC = 3cm.
   AD = √AB² - BD² = √6² - 3²
   = √36 - 9 = √27 = 3√3 cm.
   

   ∴ OD = In-radius =	1	× 3√3 = √3 cm.
   	√3

   
   ∴ Area of the in-circle = πr²
   = π × √3 × √3 = 3π sq.cm.

   Correct Option: D

   
   DB = DC = 3cm.
   AD = √AB² - BD² = √6² - 3²
   = √36 - 9 = √27 = 3√3 cm.
   

   ∴ OD = In-radius =	1	× 3√3 = √3 cm.
   	√3

   
   ∴ Area of the in-circle = πr²
   = π × √3 × √3 = 3π sq.cm.

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