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The ratio between the perimeter and the breadth of a rectangle is 5:1. If the area of the rectangle is 294 square cm, what is the length of the rectangle?
- a)12 cm
- b)15 cm
- c)19 cm
- d)21 cm
- e)None of these
Correct answer is option 'D'. Can you explain this answer?
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Verified Answer
The ratio between the perimeter and the breadth of a rectangle is 5:1....
Perimeter=2*(l+b)
Perimeter/breadth = 5/1
2*(l+b)/b = 5/1
2l+2b = 5b
l= 3/2 b.
Area =l*b= 294 sq. units.
3/2 * b2 = 294
b=14
l= 21
Perimeter/breadth = 5/1
2*(l+b)/b = 5/1
2l+2b = 5b
l= 3/2 b.
Area =l*b= 294 sq. units.
3/2 * b2 = 294
b=14
l= 21
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The ratio between the perimeter and the breadth of a rectangle is 5:1....
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The ratio between the perimeter and the breadth of a rectangle is 5:1....
Understanding the Problem
To find the length of the rectangle, we start with the given information:
- The ratio of the perimeter (P) to the breadth (b) is 5:1.
- The area (A) of the rectangle is 294 square cm.
Formulating the Equations
1. Perimeter Formula:
The perimeter of a rectangle is given by the formula:
P = 2(l + b), where l is the length.
2. Given Ratio:
From the ratio, we have:
P/b = 5/1
Therefore, P = 5b.
3. Area Formula:
The area is given by:
A = l * b.
We know A = 294 cm².
Solving the Equations
1. Substituting Perimeter:
From the perimeter equation:
5b = 2(l + b)
Rearranging gives:
5b = 2l + 2b
This simplifies to:
3b = 2l
Hence, l = (3/2)b.
2. Using the Area:
Substitute l in the area equation:
A = l * b
294 = (3/2)b * b
This leads to:
294 = (3/2)b²
Multiplying through by 2 gives:
588 = 3b²
Thus, b² = 196, and b = 14 cm.
Finding the Length
1. Calculating Length:
Now substituting b back to find l:
l = (3/2) * 14
l = 21 cm.
Conclusion
The length of the rectangle is 21 cm. Therefore, the correct option is D.
To find the length of the rectangle, we start with the given information:
- The ratio of the perimeter (P) to the breadth (b) is 5:1.
- The area (A) of the rectangle is 294 square cm.
Formulating the Equations
1. Perimeter Formula:
The perimeter of a rectangle is given by the formula:
P = 2(l + b), where l is the length.
2. Given Ratio:
From the ratio, we have:
P/b = 5/1
Therefore, P = 5b.
3. Area Formula:
The area is given by:
A = l * b.
We know A = 294 cm².
Solving the Equations
1. Substituting Perimeter:
From the perimeter equation:
5b = 2(l + b)
Rearranging gives:
5b = 2l + 2b
This simplifies to:
3b = 2l
Hence, l = (3/2)b.
2. Using the Area:
Substitute l in the area equation:
A = l * b
294 = (3/2)b * b
This leads to:
294 = (3/2)b²
Multiplying through by 2 gives:
588 = 3b²
Thus, b² = 196, and b = 14 cm.
Finding the Length
1. Calculating Length:
Now substituting b back to find l:
l = (3/2) * 14
l = 21 cm.
Conclusion
The length of the rectangle is 21 cm. Therefore, the correct option is D.
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