In light of that problem, I would like to offer my version. It could have puzzled both the American and Russian students:-
ABCD is a parallelogram with the lengths of the 2 adjacent sides being 5 cm and 10 cm. If one the altitude is 8 cm, what could be the length of the other altitude(s)
(a) 4 cm
(b) 16 cm
(c) 4 cm or 16 cm
(d) none of the above
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$\begingroup$The area of a parallelogram is the "base" times the "height." Each base has its own height, but the area will be the same whichever base you choose.
If the altitude (height) of $8$ cm goes with the side $5$ cm, then the area is $40$ square cm and the altitude on the side $10$ cm is $4$ cm.
If the altitude (height) of $8$ cm goes with the side $10$ cm, then the area is $80$ square cm and the altitude on the side $5$ cm is $16$ cm. However, we cannot have an altitude of $8$ cm if the other side is only $5$ cm (we would have a right triangle with leg $8$ and hypotenuse $5$), so this choice is not possible.
So the answer is (a), 4 cm.
$\endgroup$ 2 $\begingroup$4 cm is the answer, the topmost angle is equal to the bottom one, this implies that the triangles are similar.
Also, area is altitude times side length and 4x10=5x8.
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