Question

If the diagonals of a rhombus are 18 cm and 24 cm respectively, then its side is equal to

Answer 1

The diagonals of a rhombus are 18cm and 24 cm respectively.

we have to find side of the given rhombus.

solution : we know, rhombus is a parallelogram in which all sides are equal.

use formula,

d₁² + d₂² = 4a²

where d₁ and d₂ are diagonals and a is the side of a rhombus

here d₁ = 18cm and d₂ = 24 cm

so, (18cm)² + (24cm)² = 4a²

⇒324 cm² + 576 cm² = 4a²

⇒900 cm² = 4a²

⇒9 × 25 = a²

⇒a = 3 × 5 = 15

Therefore the side of rhombus is 15 cm

Answer 2

${\bold{\large{\underline{\pink{Formula:}}}}}$

${\bold{\sf{→}}}$ ${\boxed{\sf{d_{1} ²+d_{2} ² = 4a²}}}$

${\bold{\large{\underline{\green{Solution:}}}}}$

${\bold{\sf{→(18cm)²+(24cm)² = 4a²}}}$

${\bold{\sf{→324cm²+576cm² = 4a²}}}$

${\bold{\sf{→900cm² = 4a²}}}$

${\bold{\sf{→2a=30cm}}}$

${\bold{\sf{→}}}$ ${\boxed{\red{\sf{a=15cm}}}}$