Question : The area of the rhombus is 216 cm2 and the length of its one diagonal is 24 cm. The perimeter (in cm) of the Rhombus is:
Option 1: 52
Option 2: 60
Option 3: 120
Option 4: 100
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Correct Answer: 60
Solution :
Area of Rhombus = 216 cm
2
Length of one of the diagonals ($d_1$) = 24 cm
We know, the area ($A$) of a Rhombus = $\frac{1}{2}d_1d_2$
$⇒d_2 = \frac{2A}{d_1}$
$⇒d_2 = \frac{2×216}{24}$
$⇒d_2 = 18$ cm
Also, the diagonals of a Rhombus bisect each other at right angles.
Therefore, each side (s) of the Rhombus is given by:
s = $\sqrt{(\frac{d_1}{2})^2+(\frac{d_2}{2})^2}$
Putting the given values:
$\therefore$ s = $\sqrt{(\frac{24}{2})^2+(\frac{18}{2})^2}$ = 15 cm
$\therefore$ The perimeter, $P = 4×s= 4×15 = 60$ cm
Hence, the correct answer is 60.
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