Question

the side of a rhombus is 5cm if the length of one diagonal of the rhombus is 8cm, then find the length of the other diagonal​

Answer 1

Answer:

The diagonals of a rhombus intersect at the right angle.

half of each diagonal and the length of the side will form as a right-angle triangle.

Diagonal =8 cm.

2

1

of the diagonal =

2

8

=4 cm

∴a

2

+b

2

=c

2

⇒a

2

+4

2

=5

2

⇒a

2

−25=16

⇒a

2

=9

⇒a=

9

⇒a=3.

Length of the diagonal

2

1

of the diagonal =3 cm

the diagonal =3×2=6 cm

∴ The length of the other diagonal is 6 cm.

Answer 2

Given :

• The side of rhombus = 5 cm
• One of the length of diagonal of rhombus = 8 cm

find:-

• The length of the other diagonal

solution:-

The relation between the diagonals and sides of a rhombus is given by ,

$\\ \star \: {\boxed{\sf{\purple{ \bigg( \dfrac{d_1}{2} \bigg)^{2} + \bigg( \dfrac{d_2}{2} \bigg)^{2} = {s}^{2} }}}}$

$\\ \\ \sf{where}\begin{cases} & \sf{d_1 \& \: d_2 \: are \: diagonal \: of \: rhombus} \\ \\ & \sf{s \: is \: side \: of \: the \: rhombus}\end{cases}$

Substituting the values we have ,

$\\ : \implies \sf \bigg( \dfrac{8}{2} \bigg)^{2} + { \bigg( \dfrac{d_2}{2} \bigg) }^{2} = {(5)}^{2}$

$\\ : \implies \sf \: {(4)}^{2} + { \bigg( \dfrac{d_2}{2} \bigg)}^{2} = 25$

$\\ : \implies \sf 16 + { \bigg( \dfrac{d_2}{2} \bigg)}^{2} = 25$

$\\ : \implies \sf \: { \bigg( \dfrac{d_2}{2} \bigg)}^{2} = 25 - 16$

$\\ : \implies \sf \: { \bigg( \dfrac{d_2}{2} \bigg)}^{2} = 9$

$\\ : \implies \sf \: \bigg( \dfrac{d_2}{2} \bigg) = \sqrt{9}$

$\\ : \implies \sf \:\dfrac{d_2}{2} = 3$

$\\ : \implies \sf \:d_2 = 3 \times 2$

$\\ : \implies \sf{\underline{\boxed {\mathfrak{\pink{d_2 = 6 \: cm}}}}} \: \bigstar$

Hence ,

The length of the other diagonal of the given rhombus is 6 cm