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The length of a rectangular field is 5m more than its breadth. If the perimeter of the field is 74 m what is its length?
- a)16m
- b)17m
- c)21m
- d)23m
Correct answer is option 'C'. Can you explain this answer?
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Verified Answer
The length of a rectangular field is 5m more than its breadth. If the ...
Let the breadth be x m.
Length = (x + 5)
Perimeter of rectangle = 74
⇒ 2(x + 5 + x) = 74
⇒ 2x + 5 = 37 ⇒ 2x = 37 - 5
⇒ 2x = 32
Length = 16 + 5 = 21m
Length = (x + 5)
Perimeter of rectangle = 74
⇒ 2(x + 5 + x) = 74
⇒ 2x + 5 = 37 ⇒ 2x = 37 - 5
⇒ 2x = 32
Length = 16 + 5 = 21m
Most Upvoted Answer
The length of a rectangular field is 5m more than its breadth. If the ...
Understanding the Problem
To solve for the length of the rectangular field, we start with the information given:
- The length (L) is 5m more than the breadth (B).
- The perimeter (P) of the field is 74m.
Setting Up the Equations
1. Relationship Between Length and Breadth:
L = B + 5
2. Perimeter Formula:
The formula for the perimeter of a rectangle is:
P = 2(L + B)
Given that P = 74m, we can set up the equation:
2(L + B) = 74
Substituting the Length
- Substitute L with (B + 5) in the perimeter equation:
2((B + 5) + B) = 74
- Simplifying this:
2(2B + 5) = 74
4B + 10 = 74
Solving for Breadth
- Rearranging the equation:
4B = 74 - 10
4B = 64
B = 16m
Finding the Length
- Now, substitute B back into the equation for L:
L = B + 5
L = 16 + 5
L = 21m
Conclusion
The length of the rectangular field is 21m, which corresponds to option C.
This step-by-step breakdown demonstrates how to approach problems involving relationships between dimensions and perimeter in geometry.
To solve for the length of the rectangular field, we start with the information given:
- The length (L) is 5m more than the breadth (B).
- The perimeter (P) of the field is 74m.
Setting Up the Equations
1. Relationship Between Length and Breadth:
L = B + 5
2. Perimeter Formula:
The formula for the perimeter of a rectangle is:
P = 2(L + B)
Given that P = 74m, we can set up the equation:
2(L + B) = 74
Substituting the Length
- Substitute L with (B + 5) in the perimeter equation:
2((B + 5) + B) = 74
- Simplifying this:
2(2B + 5) = 74
4B + 10 = 74
Solving for Breadth
- Rearranging the equation:
4B = 74 - 10
4B = 64
B = 16m
Finding the Length
- Now, substitute B back into the equation for L:
L = B + 5
L = 16 + 5
L = 21m
Conclusion
The length of the rectangular field is 21m, which corresponds to option C.
This step-by-step breakdown demonstrates how to approach problems involving relationships between dimensions and perimeter in geometry.
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The length of a rectangular field is 5m more than its breadth. If the perimeter of the field is 74 m what is its length?a)16mb)17mc)21md)23mCorrect answer is option 'C'. Can you explain this answer?
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