If perimeter of a rhombus is 104 cm and length of one of its diagonals is 48 cm, then area of the rhombus (in cm2) is:
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 480
The diagonals of a rhombus bisect each other at right angles, so half of each diagonal and one side form a right-angled triangle. The area of a rhombus is half the product of its diagonals.
Side \(=\displaystyle\frac{104}{4}=26\) cm; half of the given diagonal \(=24\) cm
Half of the other diagonal \(=\sqrt{26^2-24^2}=\sqrt{676-576}=\sqrt{100}=10\) cm, so the other diagonal is 20 cm
Area \(=\displaystyle\frac{1}{2}\times48\times20=480\) cm2
