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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