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=(NP+LR)/(2) \\ MQ=(8+20)/(2) \\ MQ=(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=(MQ+KS)/(2) \\ 20=(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