Q The perimeter of parallelogram is 42 cm. Calculate the length of the sides of parallelogram.

Dear student,
We know that $ar(\parallel gm)=base\times altitude$
Let AB be of length 'l' and BC of length 'b'
Area can be calculated in two ways in viz DM as altitude and AB as base and DN as altitude and CB as base.
We equate the area from these two approaches.
So we have
$$\begin{gathered} l\times 6=b\times 8 \\ l=\frac{8}{6}b=\frac{4}{3}b \end{gathered}$$
Also perimeter of $\parallel gm$=2(l+b)
So we have
42=2(l+b)
$$\begin{gathered} l+b=21 \\ \frac{4}{3}b+b=21 \\ \frac{7}{3}b=21 \\ b=\frac{21\times 3}{7}=9 \\ l=\frac{4}{3}\times 9=12 \\ Regards \end{gathered}$$