What is the length of each side of a rhombus whose diagonals are of lengths 10 cm and 24 cm?

CBSE 8 - Maths

Asked by privacy | 12 Aug, 2021, 08:36: PM

Find the length of each side of a rhombus whose diagonals are 24cm and 10cm long. 

Let ABCD be the rhombus with diagonals (AC = 24 cm and BD = 10 cm) meeting at O.We know that the diagonals of a rhombus bisect each other at angles.

Applying Pythagoras theorem in right-angled AOB, we get: 

`AB^2=AO^2+BO^2=12^2+5^2` 

`AB^2=144+25=169` 

`AB=sqrt169=13 cm` 

Hence, the length of each side of the rhombus is 13 cm.

Concept: Basic Proportionality Theorem (Thales Theorem)

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