Question

Construct a rhombus $ABCD$ where $AC=6cm$ and $BD=7cm.$ Then, perimeter of rhombus $ABCD$ is:

• A. $16.2$ cm
• B. $18.7$ cm
• C. $17.8$ cm
• D. $18.4$ cm

Answer 1

The correct option is D $18.4$ cm

1. Draw a diagonal $AC=6cm$.

2. Draw a perpendicular bisector of $AC$, let the perpendicular bisector and $AC$ intersects at $O$ ($\because$ Diagonals of rhombus intersects at right angle)

3. Taking $O$ as centre and half of the length of another diagonal (i.e $3.5cm$) as radius, mark arc on the perpendicular bisector at both sides of $AC$. Name these intersection points as $B$ and $D$

4. Join $AB,AD,BC,CD$.

5. $ABCD$ is the required rhombus.

6. Measure the length of any one side ($\because$ All sides of rhombus are equal), which come out to be $4.6cm$

Perimeter of rhombus $=4\times$ side $=4\times 4.6=18.4cm$