Question : $ABCD$ is a parallelogram in which $AB = 7 \operatorname{cm}, BC = 9 \operatorname{cm}$, and diagonal $AC = 8 \operatorname{cm}$. What is the length (in cm) of the other diagonal?
Option 1: $14$
Option 2: $14\sqrt{2}$
Option 3: $7$
Option 4: $7\sqrt{2}$
Correct Answer: $14$
Solution :
Given: AC = 8 cm, AB = 7 cm, and BC = 9 cm
In parallelogram $ABCD$,
The formula of diagonals is
$AC^2 + BD^2 = 2(AB^2 + BC^2)$
$\Rightarrow 8^2 + BD^2 = 2(7^2 + 9^2)\\$
$\Rightarrow 64 + BD^2 = 2(49 + 81) = 260\\$
$\Rightarrow BD^2 = 260 - 64 = 196\\$
$\Rightarrow BD = 14 \text{ cm}\\$
Hence, the correct answer is $14$ cm.
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