Tia used a photocopier to dilate the design for a monorail track system. The figure shows the design and its photocopy: Two irre
gular quadrilaterals ABCD and EFGH are drawn. EFGH is the photocopy of design ABCD. AB measures 17 meters, BC measures 14 meters. No dimensions on EFGH are shown. The ratio of DA:HE is 1:2. What is the length, in meters, of side FG on the photocopied image?
2 answers:
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Prove:
Using mathemetical induction:
P(n) =
for n=1
P(n) = = 6
It is divisible by 2 and 3
Now, for n=k,
P(k) =
Assuming P(k) is divisible by 2 and 3:
Now, for n=k+1:
P(k+1) =
P(k+1) =
P(k+1) =
Since, we assumed that P(k) is divisible by 2 and 3, therefore, P(k+1) is also
divisible by 2 and 3.
Hence, by mathematical induction, P(n) = is divisible by 2 and 3 for all positive integer n.