86. In a trapezium ABCD, AB || CD, AB < CD, CD = 6 cm and distance between the parallel sides is 4 cm. If the area of ABCD is 16 cm², then AB is
    

1. 1. 1 cm
      

   
   
   

   2. 2 cm
      

   
   
   

   3. 3 cm
      

   
   
   

   4. 8 cm

   
   
   

---

1. View Hint View Answer Discuss in Forum

   
   

   Area of the trapezium ABCD =	1	(AB + CD) × AE
   	2

   
   

   ⇒ 16 =	1	(AB + 6) × 4
   	2

   
   ⇒ 16 = 2(AB + 6)
   ⇒ AB + 6
   

   =	16	= 8 ⇒ AB = 8 – 6 = 2 cm.
   	2

   Correct Option: B

   
   

   Area of the trapezium ABCD =	1	(AB + CD) × AE
   	2

   
   

   ⇒ 16 =	1	(AB + 6) × 4
   	2

   
   ⇒ 16 = 2(AB + 6)
   ⇒ AB + 6
   

   =	16	= 8 ⇒ AB = 8 – 6 = 2 cm.
   	2

---

87. ∆ABC is similar to ∆DEF. If the ratio of similar sides is k : 1, the ratio of their areas is
    

1. 1. k² : 1
      

   
   
   

   2. 2k: 1

   
   
   

   3. k²	: 1
      2

   
   
   

   4. 2k² : 1

   
   
   

---

1. View Hint View Answer Discuss in Forum

   
   ∆ABC ~ ∆DEF
   

   ∴	Area of ∆ABC	=	BC²	=	k²	= k² : 1
   	Area of ∆DEF		DE²		1

   Correct Option: A

   
   ∆ABC ~ ∆DEF
   

   ∴	Area of ∆ABC	=	BC²	=	k²	= k² : 1
   	Area of ∆DEF		DE²		1

---

---

88. The height of an equilateral triangle is 18 cm. Its area is

1. 1. 36√3 square metre
      

   
   
   

   2. 108√3 square cm.
      

   
   
   

   3. 108 square cm.
      

   
   
   

   4. 96√3 square metre

   
   
   

---

1. View Hint View Answer Discuss in Forum

   Height of equilateral triangle =	√3	× side
   	2

   
   

   ⇒ 18 =	√3	× side
   	2

   
   

   ⇒ side =	18 × 2	= 12√3 cm.
   	√3

   
   

   ∴ Area of triangle =	√3	= side²
   	4

   
   

   =	√3	× 12√3 × 12√3
   	4

   
   = 108√3 sq. cm.

   Correct Option: B

   Height of equilateral triangle =	√3	× side
   	2

   
   

   ⇒ 18 =	√3	× side
   	2

   
   

   ⇒ side =	18 × 2	= 12√3 cm.
   	√3

   
   

   ∴ Area of triangle =	√3	= side²
   	4

   
   

   =	√3	× 12√3 × 12√3
   	4

   
   = 108√3 sq. cm.

---

89. The length and breadth of a rectangular piece of a land are in a ratio 5 : 3. The owner spent Rs. 6000 for surrounding it from all sides at Rs. 7.50 per metre. The difference between its length and breadth is
    

1. 1. 50 metre
      

   
   
   

   2. 100 metre
      

   
   
   

   3. 150 metre
      

   
   
   

   4. 250 metre

   
   
   

---

1. View Hint View Answer Discuss in Forum

   Perimeter of rectangular land =	6000	= 800 metre
   	7.5

   
   Length = 5x metre
   Breadth = 3x metre
   ∴ 2 (5x + 3x) = 800
   

   ⇒ 16x = 800 ⇒ x =	800	= 50
   	16

   
   ∴ Required difference = 5x – 3x = 2x metre
   = (2 × 50) metre = 100 metre

   Correct Option: B

   Perimeter of rectangular land =	6000	= 800 metre
   	7.5

   
   Length = 5x metre
   Breadth = 3x metre
   ∴ 2 (5x + 3x) = 800
   

   ⇒ 16x = 800 ⇒ x =	800	= 50
   	16

   
   ∴ Required difference = 5x – 3x = 2x metre
   = (2 × 50) metre = 100 metre

---

---

90. The ratio between the area of a square and that of a circle, when the length of a side of the square is equal to that of the diameter of the circle, is (Take, π = 22/7)
    

1. 1. 14 : 11
      

   
   
   

   2. 28 : 11
      

   
   
   

   3. 7 : 22
      

   
   
   

   4. 22 : 7

   
   
   

---

1. View Hint View Answer Discuss in Forum

   Side of square = x metre
   Radius of circle = x/2 metre
   

   ∴	Area of square	=	x²
   	Area of circle		π		x		²
   					2

   
   

   =	x²
   	22	×	x²
   	7		2

   
   

   =	28	=	14
   	22		11

   
   = 14 : 11

   Correct Option: A

   Side of square = x metre
   Radius of circle = x/2 metre
   

   ∴	Area of square	=	x²
   	Area of circle		π		x		²
   					2

   
   

   =	x²
   	22	×	x²
   	7		2

   
   

   =	28	=	14
   	22		11

   
   = 14 : 11

---