Question

the diagonal Rhombus are 30 cm and 60 cm long find its perimeter​

Answer 1

Answer:

Step-by-step explanation:

Hey dear!!

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Diagonals of the rhombus = 30cm, 40cm

Since the diagonals intersect each other in the centre of the rhombus, they create 4 right angles.

So, we need to divide the diagonals by 2 in order to get the base and height of one right angle.

30/2 = 15cm

40/2 = 20cm

So, the height and base of the rhombus is 15cm and 20cm.

Now, using the Pythagorean theorem, we can find out the length of the hypotenuse that is the side of the rhombus.

The Pythagorean theorem states that the sum of the squares of the base and height in a 'right-angled triangle' is equal to the square on the hypotenuse.

So,

(s)^2 = (20)^2 + (15)^2

(s)^2 = 400 + 225

(s)^2 = 625

s = (625)^2

s = 25cm

Therefore, perimeter of the rhombus = 4 × s

= 4 × 25

= 100 cm

Therefore, the perimeter of the rhombus is 100 cm.

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Hope helped!

Answer 2

Step-by-step explanation:

Let rhombus ABCD be the rhombus with diagonals AC = 60 CM and DB = 30 CM

The diagonals of a rhombus are perpendicular bisectors of each other, thus giving us four right triangles and splitting each diagonal in half.

In triangle AOB,

By Pythagoras theorem (since angle AOB is 90°),

AB² = AO² + BO²

AB² = 30² + 15²

= 900 + 225

AB = √1125

= 33.5 CM

Perimeter of rhombus

P = 4a

= 4 × 33.5

= 134 CM