Question

5.
In the given figure ABCD is a rhombus such that BD = 8 cm. Find the length of BC.
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Answer 1

Given: In the given figure ABCD is a rhombus such that BD = 8 cm.

To find: The length of BC.

Solution:

As evident from the figure, the rhombus has all its sides equal. Let the sides of the rhombus be equal to x. The points B, C and D form a right-angled triangle where BC is the base, CD is the perpendicular and BD is the hypotenuse. Using the Pythagoras Theorem, the value of x can be found as follows.

$BD^{2} = BC^{2} + CD^{2}$

$8^{2} = x^{2} + x^{2}$

$2x^{2} = 64$

$x = 5.66$

Therefore, the length of BC is 5.66 cm.