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Sambhaji Maharaj

In parallelog...

Question

In parallelogram $A B C D$ , its diagonals intersect at point $O$ . If $O A = 6 c m$ and $O B = 7.5 c m$ , find the lengths of $A C$ and $B D$ .

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Solution

Diagonals of a parallelogram bisect each other .

Hence, $O A = \frac{1}{2} A C$ and $O B = \frac{1}{2} B D$
It is given that $O A = 6 c m$ and $O B = 7.5 c m$
So,
$O A = \frac{1}{2} A C$
$\Rightarrow A C = 2 \times O A = 2 \times 6 = 12 c m$
And,
$O B = \frac{1}{2} B D$
$\Rightarrow B D = 2 \times O B = 2 \times 7.5 = 15 c m$
Therefore, lengths of $A C$ and $B D$ is equal to $12 c m and 15 c m$ respectively.

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