The perimeter of a rectangle is $44\text{ cm}$. Its length is $2\text{ cm}$ more than twice its breadth. The length of the rectangle is:
(a) $16\text{ cm}$
(b) $14\text{ cm}$
(c) $15\text{ cm}$
(d) $18\text{ cm}$
Step-by-Step Solution
Key Concept: If length is $4\text{ cm}$ more than twice breadth, $L + B = 22$ and $L = 2B + 4 \Rightarrow 3B = 18 \Rightarrow B = 6, L = 16$.
$2(L + B) = 44 \Rightarrow L + B = 22$. [0.5 Mark]
Substitute $L = 2B + 4 \Rightarrow 2B + 4 + B = 22 \Rightarrow 3B = 18 \Rightarrow B = 6\text{ cm}, L = 16\text{ cm}$. [0.5 Mark]
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🎯 Official CBSE Marking Scheme:
Setting up $L + B = 22$: 0.5 Mark
Solving $L = 16\text{ cm}$: 0.5 Mark
Correct Answer: $16\text{ cm}$