Let ABCD be a parallelogram and E be the midpoint of BC. The diagonal BD and line segment AE intersects at F. If BF = 2.4 cm, then what is BD equal to ?

Explanation

Triangles ADF and EBF are similar because AD || BE. Since E is the midpoint of BC, BE = \frac{1}{2}BC = \frac{1}{2}AD. Therefore, the ratio of similitude is 1:2. This implies FD = 2 \times BF = 2 \times 2.4 = 4.8 cm. Total diagonal BD = BF + FD = 2.4 + 4.8 = 7.2 cm.

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