Question : One side of a rhombus is 13 cm and one of its diagonals is 24 cm. What is the area (in cm2) of the rhombus?
Option 1: 120
Option 2: 90
Option 3: 30
Option 4: 60
Correct Answer: 120
Solution :
Side of the rhombus = 13 cm
One of the diagonals = 24 cm
$side^2 = (\frac{d_1}{2})^2+(\frac{d_2}{2})^2$
⇒ $13^2=(\frac{24}{2})^2+(\frac{d_2}{2})^2$
⇒ $169=144+(\frac{d_2}{2})^2$
⇒ $(\frac{d_2}{2})^2=25$
⇒ $\frac{d_2}{2}=5$
⇒ $d_2=10$
Area of a rhombus = $\frac{d_1 × d_2}{2}$
= $\frac{24\times10}{2}$
= $120\ cm^2$
Hence, the correct answer Is 120.
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