Question

The perimeter of a rhombus is 100 cm. Its one diagonal is 48 cm. Its other diagonal is ______.

विकल्प

• 30 cm

• 24 cm

• 14 cm

• 18 cm

Answer 1

The perimeter of a rhombus is 100 cm. Its one diagonal is 48 cm. Its other diagonal is 14 cm.

Explanation:

The perimeter of the rhombus is 100 cm,

So each side is: 

Side = `"Perimeter"/4` 

= `100/4` 

= 25 cm

One diagonal is given as 48 cm.

The diagonals of a rhombus bisect each other at right angles,

So each half of this diagonal is `48/2` = 24 cm.

In the right triangle formed by half of each diagonal and the side of the rhombus, by Pythagoras theorem:

(Half of other diagonal)² + (24)² = (25)² 

Let x be half of the other diagonal: x² + 24² 

= 25²x² + 576 

= 625x² 

= 49x 

= 7 cm

So the other diagonal is 2x = 2 × 7 = 14 cm.

Therefore, the other diagonal is 14 cm.