The ratio of the length and the breadth of a rectangle is 4 : 3 and the area of the rectangle is 6912 sq cm. Find the ratio of the breadth and the area of the rectangle?
A)1 : 96 B)1 : 48 C)1 : 84 D)1 : 68

• 6912=4x*3x
  6912=12x*x
  X^2 = 576
  X = 24
  6912=3*x
  6912=72
  72/6912 = 1 : 96
• 4 years agoHelpfull: Yes(4) No(0)
• given l/b=4/3,
  so l=4b/3
  and area=lb=6912,
  [4b/3]b=6912
  b^2=5184
  b=72
  b/area=72/6912
  =1:96
  option(A)
• 3 years agoHelpfull: Yes(2) No(0)
• l*b=6912
  l/b=4/3
  l=4*b/3
  b^2=6912*3/4
  b=72
  72/6912=1/96=1:96
• 4 years agoHelpfull: Yes(0) No(0)
• area of rectangle=l*b
  4x*3x=6912
  x=24
  breadth=24*3=72
  breadth:area of a rectangle=72:6912=1:96
• 4 years agoHelpfull: Yes(0) No(0)
• Area=3x *4x =12x^2
  6912=12x^2
  X=24
  the ratio of breadth and area=3x/12x^2=1/4x=1/4*24=1/96
• 4 years agoHelpfull: Yes(0) No(0)
• let ratio be 4x:3x
  area of rectangle=4x*3x=12x^2=6912
  x=24
  then breadth=3*24=72
  ratio=72/6912=1:96
• 3 years agoHelpfull: Yes(0) No(0)
• 4x*3x/12x=1/4x
  x=96
  1:96
• 3 years agoHelpfull: Yes(0) No(0)
• A)1 : 96
  we can find the actual value of length and breadth by taking area of rectangle formula
  so, Breadth=72, therefore 72:6912 = 1:96
• 2 years agoHelpfull: Yes(0) No(0)
• Area = Lxb
  area = 4x X 3x = 6912
  x = 24
  b = 72
  area/breadth = 1 : 96
• 1 year agoHelpfull: Yes(0) No(0)
• Assume const k
  4k * 3k = 6912
  12k*2 = 6912
  K =24
  24*3:6912=1:96
• 1 year agoHelpfull: Yes(0) No(0)
• l=4x
  b=3x
  lb=6912
  4x * 3x =6912
  12x^2 = 6912
  x^2=576
  x=24
  b=3(24)=72
  Area=6912
  72:6912
  1:96
• 3 Months agoHelpfull: Yes(0) No(0)
• Given:
  - The ratio of length to breadth is 4:3.
  - The area of the rectangle is 6912 sq cm.
  
  We need to find the ratio of the breadth to the area.
  
  #### Steps:
  
  1. **Use the ratio of the sides**:
  The area of the rectangle is the product of its length and breadth. If the ratio of length to breadth is 4:3, the area formula based on this ratio becomes:
  [
  text{Area} = 4x times 3x = 12x^2
  ]
  where (x) is the common multiple.
  
  2. **Find (x^2)** using area**:
  The area is given as 6912 sq cm, so:
  [
  12x^2 = 6912 quad Rightarrow quad x^2 = frac{6912}{12} = 576 quad Rightarrow quad x = sqrt{576} = 24
  ]
  
  3. **Find the breadth**:
  The breadth (= 3x = 3 times 24 = 72 , text{cm}).
  
  4. **Direct shortcut formula for ratio**:
  To find the ratio of the breadth to the area, use the shortcut:
  [
  text{Ratio of Breadth to Area} = frac{text{Breadth}}{text{Area}} = frac{72}{6912}
  ]
  Simplifying:
  [
  frac{72}{6912} = frac{1}{96}
  ]
  
  ### Final Answer:
  The ratio of the breadth to the area is ( boxed{1 : 96} ).
  
  This method avoids excessive steps and directly focuses on solving the problem using the given ratios, making it more suitable for aptitude questions.
• 2 Months agoHelpfull: Yes(0) No(0)