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# Trapezium watch

1. A trapezium has upper base a, lower base b, and height h. It is divided by horizontal lines (parallel to the bases) into n smaller trapezia of equal area. The uppermost smaller trapezium (i.e. the one that has upper base a) has lower base k. Find n in terms of a, b, and k.

I tried considering the case n=2 in which case k is the root mean square of a and b, but this doesn't seem to generalise. Approaches involving similar triangles also didn't seem to work. Any suggestions?
2. (Original post by Prasiortle)
A trapezium has upper base a, lower base b, and height h. It is divided by horizontal lines (parallel to the bases) into n smaller trapezia of equal area. The uppermost smaller trapezium (i.e. the one that has upper base a) has lower base k. Find n in terms of a, b, and k.

I tried considering the case n=2 in which case k is the root mean square of a and b, but this doesn't seem to generalise. Approaches involving similar triangles also didn't seem to work. Any suggestions?
That's a nice problem.

You can consider a trapezium with two right angles. Doing this allows you to make use of similar triangles.

The trapezium at the top has 1/n the area of the whole trapezium. Use the slider to change n.

Spoiler:
Show

There's a solution to the problem on my website.

4. (Original post by BuryMathsTutor)

The trapezium at the top has 1/n the area of the whole trapezium. Use the slider to change n.

Spoiler:
Show

There's a solution to the problem on my website.

Can u please explain why my thread was deleted? Was there a mistake? If so could you kindly explain rather than just deleting me. Think it is very arrogant

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