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The ratio the length and the breadth of a rectangle is 4 : 3. The area of the rectangle is 192 cm^{2}cm2. What will be its perimeter ?
- a)56 cm
- b)46 cm
- c)28 cm
- d)36 cm
Correct answer is option 'A'. Can you explain this answer?
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Verified Answer
The ratio the length and the breadth of a rectangle is 4 : 3. The area...
Given, l/b=3/4....(1)
l x b=192....(2)
On solving (1) and (2) we get, l=16 and b=12
Thus perimeter=2(l + b)=2(16 + 12)=56cm
Most Upvoted Answer
The ratio the length and the breadth of a rectangle is 4 : 3. The area...
Understanding the Problem
To find the perimeter of a rectangle given its area and the ratio of its length and breadth, we start by defining the variables based on the ratio provided.
Step 1: Define Length and Breadth
- The ratio of length (L) to breadth (B) is 4:3.
- Let the length be 4x and the breadth be 3x, where x is a common factor.
Step 2: Calculate Area
- The area of the rectangle is given by the formula: Area = Length × Breadth.
- Using our definitions: Area = (4x) × (3x) = 12x².
Step 3: Set Up the Equation
- We know the area is 192 cm², so we set up the equation: 12x² = 192.
Step 4: Solve for x
- Dividing both sides by 12 gives: x² = 16.
- Taking the square root: x = 4.
Step 5: Find Length and Breadth
- Now substituting x back:
- Length (L) = 4x = 4(4) = 16 cm.
- Breadth (B) = 3x = 3(4) = 12 cm.
Step 6: Calculate Perimeter
- The perimeter (P) of a rectangle is calculated using the formula: P = 2(L + B).
- Substituting the values: P = 2(16 + 12) = 2(28) = 56 cm.
Conclusion
The perimeter of the rectangle is 56 cm, which corresponds to option 'A'.
To find the perimeter of a rectangle given its area and the ratio of its length and breadth, we start by defining the variables based on the ratio provided.
Step 1: Define Length and Breadth
- The ratio of length (L) to breadth (B) is 4:3.
- Let the length be 4x and the breadth be 3x, where x is a common factor.
Step 2: Calculate Area
- The area of the rectangle is given by the formula: Area = Length × Breadth.
- Using our definitions: Area = (4x) × (3x) = 12x².
Step 3: Set Up the Equation
- We know the area is 192 cm², so we set up the equation: 12x² = 192.
Step 4: Solve for x
- Dividing both sides by 12 gives: x² = 16.
- Taking the square root: x = 4.
Step 5: Find Length and Breadth
- Now substituting x back:
- Length (L) = 4x = 4(4) = 16 cm.
- Breadth (B) = 3x = 3(4) = 12 cm.
Step 6: Calculate Perimeter
- The perimeter (P) of a rectangle is calculated using the formula: P = 2(L + B).
- Substituting the values: P = 2(16 + 12) = 2(28) = 56 cm.
Conclusion
The perimeter of the rectangle is 56 cm, which corresponds to option 'A'.
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The ratio the length and the breadth of a rectangle is 4 : 3. The area of the rectangle is 192cm^{2}cm2. What will be its perimeter ?a)56 cmb)46 cmc)28 cmd)36 cmCorrect answer is option 'A'. Can you explain this answer?
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