Q66 / 180 · KCET 2024 · Mathematics

The length of a rectangle is five times the breadth. If the minimum perimeter of the rectangle is 180 cm , then

A
Breadth $\leq 15 \mathrm{~cm}$
Correct answer
B
Breadth $\geq 15 \mathrm{~cm}$
C
Length $\leq 15 \mathrm{~cm}$
D
Length $=15 \mathrm{~cm}$

Solution

Since, perimeter $\geq 180$ $\Rightarrow 2$ (length + breadth) $\geq 180$ $\Rightarrow 5$ breadth + breadth $\geq 90$ $[\because$ length $=5$ breadth $]$ $\Rightarrow 6$ breadth $\geq 90$ Hence, breadth $\geq 15$

Hence, the correct answer is option: 'B'.

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