Question

The length of a rectangle is three times the breadth. If the minimum perimeter of the rectangle is 160 cm, then

• A. $\mathrm{breadth}>20\mathrm{cm}$
• B. $\mathrm{breadth}\ge 20\mathrm{cm}$
• C. $\mathrm{length}<20\mathrm{cm}$
• D. $\mathrm{length}\le 20\mathrm{cm}$

Answer 1

The correct option is B $\mathrm{breadth}\ge 20\mathrm{cm}$

Let x cm be a breadth of the rectangle. Therefore, length = 3x cm.
Since, the minimum perimeter is 160 cm.
$\therefore \mathrm{Perimeter}\ge 160\Rightarrow 2(\mathrm{length}+\mathrm{breadth})\ge 160\Rightarrow 2(3x+x)\ge 160\Rightarrow 8x\ge 160\Rightarrow x\ge 20$