Question

I need help finding the bottom layer of the cake

Answer 1

In a trpezium, the median line is always parallel to the bases. The expression for the length of the median of trapezium is :

$\text{length of mediam=}\frac{Sum\text{ of parallel sides}}{2}$

In the trapezium: NM = ML=LK=PQ=QR=RS

we have : NP = 8, LR =20

Conisder the case of trapezium NPLR, where MQ is the median

From the expression of the length of median:

$\begin{gathered} MQ=\frac{NP+LR}{2} \\ MQ=\frac{8+20}{2} \\ MQ=\frac{28}{2} \\ MQ=14 \end{gathered}$

Now, consider the case of trapezium MQSK, where LR is act as median, MQ= 14, LR =20

From the expression of the length of median

$\begin{gathered} \text{length of median=}\frac{Sum\text{ of parallel sides}}{2} \\ LR=\frac{MQ+KS}{2} \\ 20=\frac{14+KS}{2} \\ 14+KS=40 \\ KS=40-14 \\ KS=26\text{ inches} \end{gathered}$

So, the diameter of the bottom KS is 26 inches

Answer : the diameter of the bottom KS is 26 inches