Question

14. Find the length of each side of a rhombus whose diagonals are 24 cm
and 10 cm long. ​

Answer 1

Given

length of diagonals are 24cm &10cm respectively.

To Find

Length of each side of rhombus

$\sf\huge\bold{\underline{\underline{{Solution}}}}$

We know that diagonals of rhombus bisects each other at right angle.It means a diagonal should be equal to the two bisected parts.

from above figure :

Let AC & BD be two diagonals whose length be 24cm &10cm respectively.

Now ,AC and BD bisects each other e.g

AC=AO+OC

BD=BO+OD

AO=1/2×AC=1/2×24=12cm

BO=1/2×BD=1/2×10=5cm

Now,in ∆AOB two sides we find above

AO and BO

In∆AOB

By applying Pythagoras theorem:

AB²=OA²+OB²

AB²=12²+5²

AB²=144+25=169

AB=√169=13cm

AB=13cm

We know that length of each sides in rhombus is equal.

So, 13 cm be the length of each sides of rhombus