Question

The lengths of the diagonals of a rhombus are 30 cm and 40 cm. Find the side of the rhombus.

Answer 1

Answer:

The side of the given rhombus is 25 cm.

Step-by-step explanation:

Given:

The lengths of diagonals AC and BD of rhombus ABCD are 30 cm and 40 cm.

Let the diagonals AC and CD of the rhombus ABCD meet at point O.

∠ AOD = 90º = ∠ BOC

[Diagonals of a rhombus bisect each other at perpendicular angles]

AO = OC and BO = OD .

AO = 1/2 *AC = 1/2 * 30 = 15 cm

OD = 1/2 *BD = 1/2 * 40 = 20 cm

Therefore,  

In ΔAOD, by applying Pythagoras' theorem

AD² = AO² + OD²

AD² = 15² + 20²

AD² = 225 + 400

AD² = 625

AD =√625

AD  = 25 cm

Side of rhombus (AD) = 25 cm

Hence, the side of the given rhombus is 25 cm.

HOPE THIS ANSWER WILL HELP YOU ..

Answer 2

☺HELLO☺

ANSWER:-

Let ABCD be a rhombus with AC and BD as diagonals of length 30 cm and 40 cm.

So,

1/2 of 30 =15 cm

1/2 of 40=20 cm

Let us take the side of the rhombus be 'x'.

By pythagoras theorem,

${x}^{2} = {15}^{2} + {20}^{2}$

${x}^{2} = 225 + 400$

${x}^{2} = 625$

$x = \sqrt{625}$

$x = 25 \: cm$

So, the side of the rhombus =25 cm

HOPE IT HELPS UHH

#CHEERS