Lengths of the diagonals of a given rhombus are 16 cm and 12cm. Find the length of each side of the rhombus.

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10 cm

12 cm

9 cm

8cm

answer is A.

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Detailed Solution

Given is a rhombus with length of diagonals as 16 cm and 12cm.
Let ABCD be given rhombus
Question Image

Δ O B C

, the

∠ B O C = 90 ∘

, because diagonals of a rhombus intersect at right angles.

B C 2 = O B 2 + O C 2

(By Pythagoras theorem)
We are given that the diagonals of the rhombus are 16cm and 12cm.
So, 2OB = BD,
2OC = AC.

B C 2 = 62 + 82

B C 2 = 36 + 64 B C 2 = 100 B C 2 = 100

B C = 10 c m

And we know that all the sides of a rhombus are equal.

A B = B C = C D = D A = 10 c m

Hence, 1 is the correct choice.

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