Question

If two sides of a parallelogram are $6$ and $8$ and one diagonal is $7$, what is the length of the other diagonal?

• A. $\sqrt{123}$
• B. $\sqrt{11}$
• C. $\sqrt{131}$
• D. $\sqrt{151}$
• E. $9$

Answer 1

Answer: (D)

$\sqrt{151}$

Given, two sides of parallelogram are $6$ and $8$ and one diagonal $7$.

$\cos \theta =\frac{6^2+8^2-7^2}{2\times 6\times 8}=\frac{36+64-49}{96}=\frac{51}{96}$
Now let the other diagonal length be $a$
We have $a^2=6^2+8^2-96\cos (180-\theta )=100+51=151$
$\Rightarrow a=\sqrt{151}$