Question

A parallelogram has sides 10m and 12m and an angle of 45°. Find the distance between the 12m-sides.

Answer 1

Answer:

The distance between 12m-sides is $5\sqrt{2}m$.

Step-by-step explanation:

It is given that the parallelogram has sides 10m and 12m and an angle of 45°.

Draw an altitude from one 12m side to another 12 m side as shown in below figure.

The opposite angles of parallelogram are same. Two angles are obtuse angles and two are acute angle.

Since angle C is acute angle therefore it must be 45 degree.

$\sin\theta=\frac{perpendicular}{hypotenuse}$

$\sin C=\frac{BE}{BC}$

$\sin(45^{\circ})=\frac{d}{10}$

$\frac{1}{\sqrt{2}}=\frac{d}{10}$

$\frac{10}{\sqrt{2}}=d$

$\frac{10}{\sqrt{2}}\times \frac{\sqrt{2}}{\sqrt{2}}=d$

$\frac{10\sqrt{2}}{2}=d$

$5\sqrt{2}=d$

Therefore the distance between 12m-sides is $5\sqrt{2}m$.