836. Sides of a parallelogram are in the ratio 5 : 4. Its area is 1000 sq. units. Altitude on the greater side is 20 units. Altitude on the smaller side is
     

1. 1. 30 units
      

   
   
   

   2. 25 units
      

   
   
   

   3. 10 units
      

   
   
   

   4. 15 units

   
   
   

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1. View Hint View Answer Discuss in Forum

   Using Rule 11,
   Let the sides of parallelogram be 5x and 4x. Base × Height
   = Area of parallelogram
   ∴ 5x × 20 = 1000
   

   ⇒ x =	1000	= 10
   	5 × 20

   
   ⇒ Sides = 50 and 40 units
   ∴ 40 × h = 1000
   

   ⇒ h =	1000	= 25 units
   	40

   Correct Option: B

   Using Rule 11,
   Let the sides of parallelogram be 5x and 4x. Base × Height
   = Area of parallelogram
   ∴ 5x × 20 = 1000
   

   ⇒ x =	1000	= 10
   	5 × 20

   
   ⇒ Sides = 50 and 40 units
   ∴ 40 × h = 1000
   

   ⇒ h =	1000	= 25 units
   	40

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837. The perimeter of a rhombus is 40 cm and the measure of an angle is 60°, then the area of it is :
     

1. 1. 100√3 cm²
      

   
   
   

   2. 50√3 cm²
      

   
   
   

   3. 160√3 cm²
      

   
   
   

   4. 100 cm²

   
   
   

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1. View Hint View Answer Discuss in Forum

   Using Rule 12,
   
   

   Side =	40	= 10 cm
   	4

   
   AB = AD = 10 cm
   ∠ABD = ∠ADB = 60°
   

   ∴ Area of the rhombus = 2 ×	√3	× (AB)²
   	4

   
   

   ∴ Area of the rhombus = 2 ×	√3	× 10 × 10
   	4

   
   = 50√3 cm²

   Correct Option: B

   Using Rule 12,
   
   

   Side =	40	= 10 cm
   	4

   
   AB = AD = 10 cm
   ∠ABD = ∠ADB = 60°
   

   ∴ Area of the rhombus = 2 ×	√3	× (AB)²
   	4

   
   

   ∴ Area of the rhombus = 2 ×	√3	× 10 × 10
   	4

   
   = 50√3 cm²

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838. The parallel sides of a trapezium are in a ratio 2 : 3 and their shortest distance is 12 cm. If the area of the trapezium is 480 sq. cm., the longer of the parallel sides is of length :
     

1. 1. 56 cm
      

   
   
   

   2. 36 cm
      

   
   
   

   3. 42 cm
      

   
   
   

   4. 48 cm

   
   
   

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1. View Hint View Answer Discuss in Forum

   Using Rule 13,
   Let Sides of the trapezium be 2x and 3x cm
   

   ∴	1	(2x + 3x) × 12 = 480
   	2

   
   

   ⇒ 5x =	480	= 80
   	6

   
   

   ⇒ x =	80	= 16
   	5

   
   ∴ Larger side = 3x = 16 × 3 = 48 cm

   Correct Option: D

   Using Rule 13,
   Let Sides of the trapezium be 2x and 3x cm
   

   ∴	1	(2x + 3x) × 12 = 480
   	2

   
   

   ⇒ 5x =	480	= 80
   	6

   
   

   ⇒ x =	80	= 16
   	5

   
   ∴ Larger side = 3x = 16 × 3 = 48 cm

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839. If the sum of the length, breadth and height of a rectangular parallelopiped is 24 cm and the length of its diagonal is 15 cm, then its total surface area is
     

1. 1. 256 cm²
      

   
   
   

   2. 265 cm²
      

   
   
   

   3. 315 cm²
      

   
   
   

   4. 351 cm²

   
   
   

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1. View Hint View Answer Discuss in Forum

   l + b + h = 24 [given]
   l² + b² + h² = 225 [given]
   ∴ (l + b + h)²
   = l² + b² + h² + 2(lb + bh + hl)
   ⇒ (24)² = 225 + 2 (lb + bh + hl)
   ⇒ 2(lb + bh + hl)
   = 576 – 225 = 351 sq. cm.

   Correct Option: D

   l + b + h = 24 [given]
   l² + b² + h² = 225 [given]
   ∴ (l + b + h)²
   = l² + b² + h² + 2(lb + bh + hl)
   ⇒ (24)² = 225 + 2 (lb + bh + hl)
   ⇒ 2(lb + bh + hl)
   = 576 – 225 = 351 sq. cm.

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840. The perimeter of a non-square rhombus is 20 cm. One of its diagonal is 8 cm. The area of the rhombus is
     

1. 1. 28 sq cm
      

   
   
   

   2. 20 sq cm
      

   
   
   

   3. 22 sq cm
      

   
   
   

   4. 24 sq cm

   
   
   

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1. View Hint View Answer Discuss in Forum

   Using Rule 12,
   
   

   Side of rhombus =	20	= 5 cm
   	4

   
   OB = 4 cm
   OA = √5² - 4² = √9
   = 3 cm
   AC = 6 cm
   

   Area of rhombus =	1	d1d2	1	× 8 × 6 = 24 sq. cm
   	2		2

   Correct Option: D

   Using Rule 12,
   
   

   Side of rhombus =	20	= 5 cm
   	4

   
   OB = 4 cm
   OA = √5² - 4² = √9
   = 3 cm
   AC = 6 cm
   

   Area of rhombus =	1	d1d2	1	× 8 × 6 = 24 sq. cm
   	2		2

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