Question : The area of a rhombus having one side measuring 17 cm and one diagonal measuring 16 cm is:
Option 1: 280 cm2
Option 2: 180 cm2
Option 3: 240 cm2
Option 4: 210 cm2
Correct Answer: 240 cm 2
Solution :
Length of side = 17 cm
Length of a diagonal = 16 cm
The two diagonals bisect each other at 90$^\circ$ in a rhombus.
Area of rhombus = ($\frac{1}{2}$) × Product of the two diagonals
Let AC = 16 cm and BD = x cm
If the two diagonals of rhombus ABCD intersect at O then,
$AO^2 + BO^2 = AB^2$
⇒ $\left(\frac{16}{2}\right)^2 + \left(\frac{x}{2}\right)^2 = 17^2$
⇒ $64 + \left(\frac{x^2}{4}\right) = 289$
⇒ $\left(\frac{x^2}{4}\right) = 225$
⇒ $x^2= 900$
$\therefore x = 30$ cm
Area of rhombus = ($\frac{1}{2}$) × 16 × 30 = 8 × 30 = 240 cm
2
Hence, the correct answer is 240 cm
2
.
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