Question

$ABCD$ is a parallelogram $AB=14cm,BC=18cm,AC=16cm$ then the length of the other diagonal.

• A. $24cm$
• B. $28cm$
• C. $36cm$
• D. $32cm$

Answer 1

The correct option is B $28cm$

Considering $\left|\overline{a}\right|=14$, $\left|\overline{b}\right|=18$, So, $|\overline{a}-\overline{b}|=16$ and $Q=\overline{a}\wedge \overline{b}$

So, $|\overline{a}-\overline{b}|=16=\sqrt{{\left|\overline{a}\right|}^2+{\left|\overline{b}\right|}^2-2\left|\overline{a}\right|\left|\overline{b}\right|\cos \theta }$

$256=196+324-2\left(14\right)\left(18\right)\cos \theta$

So $\cos \theta =0.523$

other diagonal will be

$|\overline{a}+\overline{b}|=\sqrt{{\left|\overline{a}\right|}^2+{\left|\overline{b}\right|}^2+2\left|\overline{a}\right|\left|\overline{b}\right|\cos \theta }$

$|\overline{a}+\overline{b}|=\sqrt{{14}^2+{18}^2+2\left(14\right)\left(18\right)\left(0.523\right)}$

So, $|\overline{a}+\overline{b}|=$ other diagonal $=27.99\approx 28cm$