Question : One side of a rhombus is 13 cm and one of its diagonals is 10 cm. What is the area of the rhombus (in cm2)?
Option 1: 60
Option 2: 90
Option 3: 30
Option 4: 120
Correct Answer: 120
Solution :
Side of a rhombus, $a$ = 13 cm
Diagonal, $d_1$ = 10 cm
Let $d_2$ be the second diagonal.
So, $(\frac{d_1}{2})^2 + (\frac{d_2}{2})^2 = a^2$
⇒ $(\frac{10}{2})^2 + (\frac{d_2}{2})^2 = 13^2$
⇒ $(\frac{d_2}{2})^2 = 169-25 = 144$
⇒ $(\frac{d_2}{2}) = \sqrt{144}$
⇒ $d_2 = 12 × 2 = 24$
Now, the area of rhombus = $\frac{1}{2}d_1d_2$
= $\frac{1}{2} × 10 × 24$
= 120 cm$^2$
Hence, the correct answer is 120.
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