If the diagonals of a rhombus are 8 cm and 15 cm. Then the length of each side is ____ cm.

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Detailed Solution

If the diagonals of a rhombus are 8 cm and 15 cm. Then the length of each side is 8.5 cm.
Drawing a rhombus using given data AC = 15 cm and BD = 8 cm.
Question Image

As we know the diagonals of rhombus bisect each other at

90 °

.
So in

Δ A O B

,
Using Pythagoras theorem,

A B 2 = O A 2 + O B 2 ⇒ A B 2 = 1522 + 822 ⇒ A B 2 = 7.5 2 + 42 ⇒ A B 2 = 56.25 + 16 ⇒ A B 2 = 72.25 ⇒ A B = 72.25 ⇒ A B = 8.5 c m

Hence, each side of rhombus ABCD is 8.5 cm.

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