Question

PLEASE SOLVE THIS WITH FULL EXPLANATION..​

Answer 1

Question -

The length of the diagonals of the rhombus are 24 cm and 18cm respectively. Find the length of each side of the rhombus

Solution -

Let, ABCD is a rhombus and BD = 24 cm and AC= 18 cm

We know that,

Rhombus is a parallelogram and in a parallelogram diagonals bisect each other.

AC and BD bisect at O

$DO = \frac{1}{2} \times BD = \frac{1}{2} \times 24 = 12cm$

And,

$OC = \frac{1}{2} \times AC = \frac{1}{2} \times 18 = 9cm$

Now,

Applying Pythagoras theorem in triangle DOC we will get -

DO² + OC² = OD²

${(12)}^{2} + {(9)}^{2} = CD {}^{2}$

$144 + 81 = CD {}^{2}$

$225 = {CD }^{2}$

$CD = 15$

Therefore the length of each side AB= BC = CD= AD is 15 cm

Answer 2

Answer:

Question -

The length of the diagonals of the rhombus are 24 cm and 18cm respectively. Find the length of each side of the rhombus

Solution -

Let, ABCD is a rhombus and BD = 24 cm and AC= 18 cm

We know that,

Rhombus is a parallelogram and in a parallelogram diagonals bisect each other.

AC and BD bisect at O

$DO=21×BD=21×24=12cm \\ </p><p>And, \\ </p><p>OC = \frac{1}{2} \times AC = \frac{1}{2} \times 18 = 9cm \\ OC=21×AC=21×18=9cm</p><p>$

Now,

Applying Pythagoras theorem in triangle DOC we will get -

DO² + OC² = OD²

$(12)2+(9)2=CD2 \\ </p><p>144 + 81 = CD {}^{2}144+81=CD2 \\ </p><p>225 = {CD }^{2}225=CD2 \\ </p><p>CD = 15CD=15</p><p>$

Therefore the length of each side AB= BC = CD= AD is 15 cm