Question : The perimeter of a Rhombus is 60 cm and one of its diagonal is 24 cm. The area of the Rhombus is:
Option 1: 108 sq.cm
Option 2: 216 sq.cm
Option 3: 432 sq.cm
Option 4: 206 sq.cm
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Correct Answer: 216 sq.cm
Solution :
Given: The perimeter of a Rhombus is 60 cm and one of its diagonals is 24 cm.
Let $a$ cm and $b$ cm be the two diagonals of the Rhombus.
Then, perimeter = $2\sqrt{a^2+b^2}$
⇒ $60 = 2\sqrt{24^2+b^2}$
⇒ $30 = \sqrt{60^2+b^2}$
⇒ $576+b^2=900$
⇒ $b^2=324$
⇒ $b=18$
Therefore, the area of the Rhombus = $\frac{1}{2}×24×18$ = $216$ sq. cm
Hence, the correct answer is 216 sq. cm.
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