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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 216 sq. cm, what is the length of the rectangle?
- a)16 cm
- b)18 cm
- c)24 cm
- d)Data inadequate
Correct answer is option 'B'. Can you explain this answer?
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Most Upvoted Answer
The ratio between the perimeter and the breadth of a rectangle is 5: 1...
According to the question,
⇒ 2(l + b)/b = 5/1
⇒ 2l + 2b = 5b
⇒ 3b = 2l
⇒ b = (2/3) l
Given, Area = 216 cm2
So, l x b = 216
⇒ l x (2/3) l = 216.
⇒ l^2 = 324
⇒ l = 18 cm.
⇒ 2(l + b)/b = 5/1
⇒ 2l + 2b = 5b
⇒ 3b = 2l
⇒ b = (2/3) l
Given, Area = 216 cm2
So, l x b = 216
⇒ l x (2/3) l = 216.
⇒ l^2 = 324
⇒ l = 18 cm.
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Community Answer
The ratio between the perimeter and the breadth of a rectangle is 5: 1...
Given Information:
- Ratio of perimeter to breadth = 5:1
- Area of the rectangle = 216 sq. cm
Solution:
Step 1: Finding Perimeter and Breadth
Let the length of the rectangle be L cm and breadth be B cm.
Given, perimeter/breadth = 5/1
=> 2(L+B)/B = 5
=> 2L + 2B = 5B
=> 2L = 3B
Step 2: Finding Length using Area
Area of rectangle = Length * Breadth
216 = L * B
Substitute 2L = 3B in the above equation:
216 = (3/2)B * B
216 = (3/2)B^2
B^2 = 144
B = 12 cm (Breadth)
Substitute B = 12 cm in 2L = 3B:
2L = 3*12
2L = 36
L = 18 cm (Length)
Therefore, the length of the rectangle is 18 cm, which corresponds to option (b) 18 cm.
- Ratio of perimeter to breadth = 5:1
- Area of the rectangle = 216 sq. cm
Solution:
Step 1: Finding Perimeter and Breadth
Let the length of the rectangle be L cm and breadth be B cm.
Given, perimeter/breadth = 5/1
=> 2(L+B)/B = 5
=> 2L + 2B = 5B
=> 2L = 3B
Step 2: Finding Length using Area
Area of rectangle = Length * Breadth
216 = L * B
Substitute 2L = 3B in the above equation:
216 = (3/2)B * B
216 = (3/2)B^2
B^2 = 144
B = 12 cm (Breadth)
Substitute B = 12 cm in 2L = 3B:
2L = 3*12
2L = 36
L = 18 cm (Length)
Therefore, the length of the rectangle is 18 cm, which corresponds to option (b) 18 cm.
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