Question

The area of rohmbus is 216cm^2 and one of its diagonal measure s 24cm find the length of other diagonal and the length of each of its side and it's perimeter.

Answer 1

Answer:

18 cm

Step-by-step explanation:

Area of rhombus = 1/2 × D1 × D2

216 = 1/2 × 24 × x

216 = 12x

x = 216/12

x = 18 cm

Hence length of other diagonal is 18 cm

Answer 2

ANSWER:-

Given:

•The area of rhombus is 216cm².

•One diagonal of rhombus is 24cm

To find:

⚫Other diagonal of rhombus

⚫Length of its side.

⚫The perimeter of rhombus.

Solution:

We have,

•Diagonal AC= 24cm

•Area of rhombus= 216cm²

Therefore,

We know that, area of rhombus;

=) 1/2 × d1 × d2

$= > \frac{1}{2} \times 24 \times d2 = 216 \\ \\ = > 12 \times d2 = 216 \\ \\ = > d2 = \frac{216}{12} \\ \\ = > d2 = 18cm$

So,

⚫Length of other diagonal is 18cm.

We know that, diagonal of rhombus are perpendicular bisectors to each other.

angle AOB= angle BOC= angle COD= angle DOA= 90°

&

•OA= OC= 12cm

•OB= OD= 9cm

Using Pythagoras Theorem, we get;

In right ∆AOB,

=) AB² = OA² + OB²

=) AB² = 12² + 9²

=) AB² = 144 + 81

=) AB² = 225

=) AB= √225

=) AB= 15cm

So,

•The length of side of rhombus is 15cm.

We know perimeter of rhombus is;

=) 4 × side

=) 4 × 15

=) 60cm

Hope it helps ☺️