Question : The lengths of the diagonals of a rhombus are 48 cm and 20 cm. What is the perimeter of the rhombus?
Option 1: 200 cm
Option 2: 120 cm
Option 3: 100 cm
Option 4: 104 cm
Correct Answer: 104 cm
Solution :
Diagonals of a rhombus bisect each other perpendicularly.
Let’s denote the length of each side of the rhombus as a
Using Pythagoras:
a
2
= $(\frac{48}{2})^{2}$ + $(\frac{20}{2})^{2}$ = 576 + 100
= $\sqrt{676}$
⇒ a = 26
So, the length of each side is
26
⇒ Perimeter = 4a = 4 × 26 = 104 cm
Hence, the correct answer is 104 cm.
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