Question

DUIVU.
Find the area of a rhombus whose side is 5 cm and whosealtitude is 4.8 cm.
If one of its diagonals is 8 cm long, find the length of the other length of the diagonal​

Answer 1

According to the Question

As we know that,

Area of the rhombus

= Side × Length of the altitude 

Hence,

= 5 × 4.8

= 24 cm²

Also now we conclude,

Assume that,

Length of the other diagonal

= p

According to information

The area of a rhombus is 1/2 of product of diagonals

Hence

$\frac{1}{2}\times 8\times p=24$

⇒ 4p = 24

$p=\frac{24}{4}$

⇒ p = 6 cm

Therefore,

Length of the other diagonal is 6 cm

Some Properties of Rhombus :-

1. As per definition all sides of rhombus are congruent.

2. The diagonals of rhombus bisect each angles

3. The diagonals of rhombus are perpendicular bisectors of each other

Answer 2

$\huge{\underline{\underline{\red{\mathfrak{Answer :}}}}}$

$\tt Given \begin{cases} \sf{Side \: of \: Rhombus \: = \: 5 \: cm} \\ \sf{Height \: = \: 4.8 \: cm} \\ \sf{One \: Diagonal \: = \: 8 \: cm} \end{cases}$

To Find :

• Area and Length of Other diagonal

Solution :

We have formula for area of rhombus :

$\Large{\underline{\boxed{\sf{Area \: = \: Side \: \times \: height}}}}$

⇒Area = 5 * 4.8

⇒Area = 24 cm²

$\Large{\boxed{\sf{Area \: = \: 24 \: cm^2}}}$

_______________________________

let length of other diagonal be x

And also we have formula for area of rhombus

${\underline{\boxed{\sf{Area \: = \dfrac{1}{2} \:( 1st \: Diagonal \: \times \: 2nd Diagonal) }}}}$

Put values

⇒24 = ½ * 8*x

⇒24 = 4*x

⇒x = 24/4

⇒x = 6

⇒x = 6 cm

$\large{\boxed{\sf{Second \: Diagonal \: = 6 \: cm}}}$