Question

if the diagonals of a rhombus are 20 cm and 48 CM, find the length of each side ​

Answer 1

$\Huge{\boxed{\red{\mathbb{QUESTION}}}}$

If the diagonals of a rhombus are 20 cm and 48 cm, find the length of each side.

$\Huge{\boxed{\pink{\mathcal{ANSWER}}}}$

$\bold{Given\:that,}$

Diagonal 1 = 20 cm

Diagonal 2 = 48 cm

$\bold{To\:find,}$

The length of each side = ?

$\bold{We\:know\:that,}$

1. Each side of a rhombus are equal.

2. The diagonals of a rhombus intersect it each other at 90°.

Suppose, in △AOB,

[By using Pythagoras theorm, that is,

$hy^2 = AB^2 - BC^2]$,

$AB^2 = AO^2 + OB^2$

$a^2 = 10^2 + 24^2$

$a^2 = 100 + 576$

$a^2 = 676$

$a = \sqrt{676}$

a = 26 cm

But, all the sides of a triangle are same.

Therefore, all the sides are = 26 cm.

$\Huge{\boxed{\boxed{\purple{Length\:=\:26\:cm}}}}$