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September 23rd, 2016, 03:21 PM   #1
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Impossible

Consider the trapezium ABCD, as the following figure, in which the angles of the vertices A and B are straight. Knowing that the measure of AB is 4 cm and the other side measures in cm, are given on the basis of fixed constant (see figure). Determine the measure of segment BD.

Tip: Build a helper line parallel to AB and use the Pythagorean theorem.
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Samuel Leite is offline  
 
September 23rd, 2016, 03:54 PM   #2
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let H be the point of BC such that DH//AB

the pythagore theorem in the triangle DHC gives

$9a^2+16=25a^2$

which gives

$a=1 cm$

then in the trangle ABD gives

$BD=5 cm$
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