Question

the length of the diagonal of a rhombus are 24 cm and 10 cm respectively. find the length of each of its side and also find the perimeter​

Answer 1

Answer:

13cm

Step-by-step explanation:

We know that in a rhombus the diagonals bisect each other at 90∘

Refer the picture.

AC=24cm

AD=12cm

BD=10cm

BO=5cm

AB2=AD2+OB2

=122+52

=144+25

=169

AB=√169

=13cm

Hence the length of the rhombus is 13 cm.

Perimeter = 4xS [ side are equal ]

                 = 4x13 = 15cm

       Hope it is helpful. Take care.

Answer 2

Answer

First, we should find the measurement of sides of the Rhombus. We know that the diagonals intersect each other and forms four right angled triangles inside a Rhombus. Each diagonal separates each other and forms four equal lines inside the Rhombus.

So, we can find the value of the side by the property of Pythagoras theorem.

$\sf \dashrightarrow {AD}^{2} = {OA}^{2} + {OD}^{2}$

$\sf \dashrightarrow {AD}^{2} = {12}^{2} + {5}^{2}$

$\sf \dashrightarrow {AD}^{2} = 144 + 25$

$\sf \dashrightarrow {AD}^{2} = 169$

$\sf \dashrightarrow {AD}^{2} = \sqrt{169}$

$\sf \dashrightarrow {AD}^{2} = 13 \: cm$

We know that all the sides in a Rhombus measures same. So,

Perimeter of the Rhombus :

$\sf \dashrightarrow 4 \times Side$

$\sf \dashrightarrow 4 \times 13$

$\sf \dashrightarrow 52 \: cm$

Hence, the second perimeter of the Rhombus are 13 and 52 cm respectively.