Question

Each side of the rhombus measures 13 cm. If one of its diagonals measures 24 cm, find the length of the other diagonal.

Answer 1

We know that,
Rhombus is a special type of parallelogram whose all the sides are equal and the diagonals are perpendicular bisectors of each other.

Therefore, ∠AOB = 90°, AO = 12 cm

Usinge the Pythagoras theorem in triangle AOB

$\Rightarrow A{B}^2=A{O}^2+O{B}^2$

$\Rightarrow {13}^2={12}^2+O{B}^2$

$\Rightarrow O{B}^2=169-144$

$\Rightarrow O{B}^2=25$

$\Rightarrow OB=5cm$

Now,

OB = OD so, OD = 5 cm

Since, diagonal DB = DO + OB

⇒ DB = 5 + 5 = 10 cm


Therefore, The length of the other diagonal is 10 cm.