Question

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. 3 : 6912
• B. 1 : 96
• C. 4 : 6912
• D. 3 : 2304

Answer 1

Answer:

B. 1 : 96

Properties of Rectangles

• A rectangle is a quadrilateral with four right angles.

• Opposite sides of a rectangle are equal in length.

• The area of a rectangle is calculated by multiplying its length (l) and breadth (b): Area = l × b.

• The perimeter of a rectangle is calculated as: Perimeter = 2 × (l + b).

Problem Breakdown

• Given the ratio of length to breadth (l : b) is 4 : 3.

• This means we can represent the length as 4x and the breadth as 3x, where 'x' is a common multiplier.

• The area of the rectangle is given as 6912 sq cm.

• We need to find the ratio of the breadth to the area (b : Area).

Calculations

• Substitute the expressions for length and breadth into the area formula:

  • Area = (4x) × (3x)

  • 6912 = 12x²

• Solve for x²:

  • x² = 6912 / 12

  • x² = 576

• Find the value of x by taking the square root:

  • x = √576

  • x = 24

• Now, calculate the actual breadth of the rectangle:

  • Breadth (b) = 3x = 3 × 24 = 72 cm.

• The question asks for the ratio of the breadth to the area.

  • Ratio = Breadth : Area

  • Ratio = 72 : 6912

• Simplify the ratio by dividing both numbers by their greatest common divisor. In this case, divide both by 72:

  • Ratio = 72/72 : 6912/72

  • Ratio = 1 : 96