Each side of a rhombus is 13 centimetres long and one of its diagonals is 24 centimetres long. How long is the other diagonal?

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Solution

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

Given: AB = BC = CD = DA = 13 cm

Diagonal BD = 24 cm

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

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 × 5 cm = 10 cm

Thus, the length of the other diagonal is 10 cm.

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