Question

find the perimeter of a rhombus with diagonals 30 cm and 40 cm long

Answer 1

rhombus diagonal are perpendicular to each other and they bisect each other
so if ABCD is a rhombus with centre 0 then triangle AOB is right angle triangle
with OB= 15 OA=20 so using pythogorus theoram AB=25

Answer 2

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!