Question

In the rhombus ABCD the diagonals AC and BD intersect at a point O if AB = 10CM and the diagonal AC= 12CM . Find the length of the diagonal BD.

Answer 1

Answer:

Step-by-step explanation:

We know that the diagonals of rhombus intersect at right angles and bisect each other.

In right triangle AOB,

${AB}^2={OA}^2+{OB}^2$

${10}^2={6}^2+{OB}^2$

$100-36={OB}^2$

${OB}^2=100-36=64$

$OB=8\:cm$

$Now\:BD=OB+OD=8+8=16cm$

Answer 2

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$\bold{Dear\:user!!}$

$\bold{\underline{Question-}}$
In the rhombus ABCD the diagonals AC and BD intersect at a point O if AB = 10CM and the diagonal AC= 12CM . Find the length of the diagonal BD.

$\bold{\underline{Answer-}}$According to the question we know that AC and BD intersect at a point O AB = 10CM and the diagonal AC= 12CM .

now applying Pythagoras theorem

AB² = OA² + OB²

OB² = 10² - 6²

OB² = 100 - 64

OB² = 36

OB = √36

OB = 6

then, BD = OB + OD

BD = 6 + 6 = 12

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