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Half the perimeter of a rectangular room is 46 m, and its length is 6 m more than its breadth. What is the length and breadth of the room?
- a)2m, 20m
- b)2m, 3m
- c)56m, 40m
- d)26m, 20m
Correct answer is option 'D'. Can you explain this answer?
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Verified Answer
Half the perimeter of a rectangular room is 46 m, and its length is 6...
Let l and b be the length and breadth of the room. Then, the perimeter of the room = 2(l + b) metres
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From question, l = 6 + b… (1)
×2(l + b) = 46 ⟹ l + b = 46… (2)
Using Substitution method: Substituting the value of l from (1) in (2), we get
6 + b + b = 46
⇒ 6 + 2b = 46
⟹ 2b = 40
⟹ b = 20 m.
Thus, l = 26 m
Most Upvoted Answer
Half the perimeter of a rectangular room is 46 m, and its length is 6...
Step-by-step explanation:
Let the length of the room be l, the breadth be b and perimeter be P.
Given:
P/2 = 46 m
l = b + 6 m
Solution
Since P = 2(l + b), P/2 = l +b, we have following equations:
l + b = 46
l = b + 6
Substituting l in first equation:
b + 6 + b = 46
2b + 6 = 46
2b = 40
b = 20 m
Then the length is:
l = b + 6 = 20 + 6 = 26 m
Let the length of the room be l, the breadth be b and perimeter be P.
Given:
P/2 = 46 m
l = b + 6 m
Solution
Since P = 2(l + b), P/2 = l +b, we have following equations:
l + b = 46
l = b + 6
Substituting l in first equation:
b + 6 + b = 46
2b + 6 = 46
2b = 40
b = 20 m
Then the length is:
l = b + 6 = 20 + 6 = 26 m
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Community Answer
Half the perimeter of a rectangular room is 46 m, and its length is 6...
Given information:
Half the perimeter of the rectangular room = 46m
Length = Breadth + 6m
Solution:
Step 1: Formulas
Let's denote the length of the room as L and the breadth as B.
Perimeter of a rectangle = 2(L + B)
Step 2: Half the Perimeter
Half the perimeter of the rectangle = 46m
So, half the perimeter = 2(L + B) / 2 = L + B = 46
Step 3: Length in terms of Breadth
Given, Length = Breadth + 6
Substitute this into the formula derived in Step 2:
(B + 6) + B = 46
2B + 6 = 46
2B = 40
B = 20m
Step 4: Find Length
Length = Breadth + 6
Length = 20 + 6
Length = 26m
Step 5: Final Answer
Therefore, the length of the room is 26m and the breadth is 20m. So, option 'D' is the correct answer.
Half the perimeter of the rectangular room = 46m
Length = Breadth + 6m
Solution:
Step 1: Formulas
Let's denote the length of the room as L and the breadth as B.
Perimeter of a rectangle = 2(L + B)
Step 2: Half the Perimeter
Half the perimeter of the rectangle = 46m
So, half the perimeter = 2(L + B) / 2 = L + B = 46
Step 3: Length in terms of Breadth
Given, Length = Breadth + 6
Substitute this into the formula derived in Step 2:
(B + 6) + B = 46
2B + 6 = 46
2B = 40
B = 20m
Step 4: Find Length
Length = Breadth + 6
Length = 20 + 6
Length = 26m
Step 5: Final Answer
Therefore, the length of the room is 26m and the breadth is 20m. So, option 'D' is the correct answer.
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Half the perimeter of a rectangular room is 46 m, and its length is 6 m more than its breadth. What is the length and breadth of the room?a)2m, 20mb)2m, 3mc)56m, 40md)26m, 20mCorrect answer is option 'D'. Can you explain this answer?
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