Question

In a rhombus of side 10 cm, one of the diagonals is 12 cm long. The length of the second diagonal is ______.

पर्याय

• 20 cm

• 18 cm

• 16 cm

• 22 cm

Answer 1

In a rhombus of side 10 cm, one of the diagonals is 12 cm long. The length of the second diagonal is 16 cm.

Explanation:

In a rhombus the diagonals bisect each other at right angles.

Half of the given diagonal is 6 cm, so using Pythagoras on the right triangle formed by half-diagonals and a side:

10² = 6² + (half of other diagonal)² 

⇒ (half)² = 100 – 36 = 64 

⇒ half = 8

So, the full diagonal = 2 × 8 = 16 cm.