Question

the diagonal of a rhombus are 10 cm & 26cm respectively.find the length of one side of the rhombus.answer is 13.9​

Answer 1

According to the question,

Diagonal = AC = 26 cm

This AC can be written as AO + OC

We know that in a rhombus, diagonals bisect each other.

So, AO = OC = 13 cm

Similarly, BO = OD = 5 cm

Diagonals of a rhombus are perpendicular to each other.

So, 4 right angled triangles are formed namely ∆AOB, ∆AOD, ∆BOC, ∆DOC.

Consider any 1 right angled triangle.

Let's take ∆AOD

In ∆AOD,

By Pythagoras theorem,

(AD)² = (AO)² + (OD)²

→ (AD)² = (13)² + (5)²

→ (AD)² = 169 + 25

→ (AD)² = 194

→ (AD) = √194

→ (AD) = 13.9 cm

∴ Length of 1 side of rhombus = 13.9 cm