Question

if length of a diagonal of rhombus is 30 cm and its area is 240 sq cm find its perimeter​

Answer 1

Basic Concept: Diagonal of the rhombus bisect each other perpendicularly.

Remember the area of rhombus=Product of the two diagonal ÷2

Remember pythogoras property.

Now,

Given:One diagonal is 30cm

Area is 240cm^2

Find unknown diagonal first.

Using area of rhombus formula

we can find another diagonal.

Let another diagonal be" X"

According to questions,

30×X/2=240

=>30X=480

=>X=480/30

=>X=16

So, length of another diagonal is 16

We knew that diagonal bisect each other perpendicularly.

So, by Pythagoras property.

Mid point of one diagonal is 15

Another is 8

By Pythagoras property.

8^2+15^2=(length of one side)^2

64+225=(length of one side)^2

√289=(length of one side)

=>length of one side =17cm

We know that in rhombus all side are equal.

Perimeter is =4×one side

We know that one side is 17

perimeter is:4×17=68cm

so, ur answer is 68cm

Answer 2

Answer: 68 cm

Step-by-step explanation:

Step 1: Note what all values are given

Given:

Diagonal 1 = 30 cm

Area of Rhombus = 240 Sq. cm

Perimeter of Rhomus = ?

Diagonal 2 = ?

Side of Rhombus = ?

Step 2: First Find Diagonal 2

We can find the Diagonal of rhombus by the formula to find its area.

Area of rhombus = 1/2 * Diagonal 1 * Diagonal 2

240 = 1/2 * 30 * Diagonal 2

240 = 15 * Diagonal 2

240/15 = Diagonal 2

16 = Diagonal 2  

Therefore, The Diagonal 2 is 16 cm.

Step 3: Find the Side through Pythagoras Theorem

As the diagonal bisect each other and forms a right angle, We can find the side through the Pythagoras theorem.

Pythagoras Theorem:

$a^2 + b^2 = c^2$

[Now Note, One Diagonal is 30cm, To find the side through this formula we have to take the half of it. Same Applies to the second Diagonal]

$15^2 + 8^2 = c^2$

225 + 64 = $c^{2}$

√289 = c

17 = c

Therefore, The Side of the Rhombus is 17cm.

Step 4: Find the Perimeter by multiplying 4.

As Rhombus has all its 4 same, You can either multiply the side by 4 or manually add the side 4 times.

Perimeter of Rhombus = 4 * Side

= 4 *17

= 68 cm

So, The Perimeter of the Rhombus is 68 cm.