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Theorem 3: Opposite Angles in a Parallelogram Are Equal

A parallelogr...

Question

A parallelogram ABCD with diagonals AC = 12 cm and BD = 16 cm is given. What is the length of AD if the perimeter of triangle AOD is 25 cm?

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Solution

From the question, ABCD is a parallelogram.
AC = 12 cm and BD = 16 cm (Given)

AO = 6 cm = OC and DO = 8 cm = BO (Diagonals of a paralleogram bisect each other)

Perimeter of $△$ AOD = AO + OD + AD
$\Rightarrow$ 25 = 6 + 8+ AD
$\Rightarrow$ 25 = 14 + AD
$\Rightarrow$ AD = 25 - 14 = 11 cm

Length of AD = 11 cm

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