Question

The perimeter of a rhombus is 68 centimetres and the length of one of its diagonals is 30 centimetres. Find the length of the other diagonal.

Answer 1

Let the given rhombus be ABCD whose diagonals intersect at a point O.

Given: Perimeter of the rhombus = 68 cm

Diagonal BD = 30 cm

The figure for the given information can be drawn as follows:

Perimeter of the rhombus ABCD = 4 × AB

⇒ 68 cm = 4 × AB

⇒ AB =

∴ AB = BC = CD = DA = 17 cm

We know that the diagonals of a rhombus are perpendicular bisectors of each other.

∴ BO =

Also, ∠BOC = 90°

In ΔBOC, using Pythagoras theorem, we get:

∴ AC = 2 × OC = 2 × 8 cm = 16 cm

Thus, the length of the other diagonal is 16 cm.