What is the perimeter of the figure LORM? PQRS is a square. M and K are midpoints of the sides RQ and QP respectively.

$2 \sqrt{2}$ cm

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$2 \sqrt{2}$ + 1 cm

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2 + $\sqrt{2}$ cm

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$4 \sqrt{2}$ cm

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Solution

The correct option is B
$2 \sqrt{2}$ + 1 cm

To find the perimeter of the figure, we need to know the following :

LO , OR , RM and ML

LO = KL = $\frac{1}{\sqrt{2}}$ cm (Sides of square LOJK)

PS = SR = 2 cm (Sides of square PQRS)

Diagonal PR = $\sqrt{2^{2} + 2^{2}}$ = $2 \sqrt{2}$ cm

OR = Half of PR = $\frac{1}{2} \times 2 \sqrt{2}$ = $\sqrt{2}$ cm

RM = $\frac{1}{2} \times 2$ = 1 cm

ML = KL = $\frac{1}{\sqrt{2}}$ cm

$∴$ Perimeter = LO + OR + RM + ML

= $\frac{1}{\sqrt{2}}$ + $\sqrt{2}$ + 1 + $\frac{1}{\sqrt{2}}$

= $\frac{2}{\sqrt{2}}$ + $\sqrt{2}$ + 1

= $\sqrt{2}$ + $\sqrt{2}$ + 1

= $2 \sqrt{2}$ + 1 cm

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