Question

If the side of a rhombus is 15 cm and one diagonal is 24 cm then the length of the other diagonal is ______.

Options

• 18 cm

• 20 cm

• 26 cm

• 25 cm

Answer 1

If the side of a rhombus is 15 cm and one diagonal is 24 cm then the length of the other diagonal is 18 cm.

Explanation:

Side of rhombus = 15 cm

One diagonal = 24 cm

Let the other diagonal = 2x

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

So, half of each diagonal forms the sides of a right-angled triangle.

Half of one diagonal = `24/2` = 12 cm

By Pythagoras theorem,

Side² = 12² + x²

15² = 144 + x²

225 = 144 + x²

x² = 81

x = 9

Other diagonal = 2x

= 2 × 9

= 18 cm