Given that ΔSCD and ΔSAB are similar triangles, the distance across the lake is: AB = 62.4 m.
Sides of Similar Triangles
Similar triangles possess corresponding side lengths that are proportional to each other, which means the ratio of their corresponding sides are equal.
Thus, since ΔSCD is similar to ΔSAB, therefore:
SD/SB = CD/AB
6/(6 + 66) = 5.2/AB
6/72 = 5.2/AB
AB = (72×5.2)/6
AB = 62.4 m
Therefore, given that ΔSCD and ΔSAB are similar triangles, the distance across the lake is: AB = 62.4 m.
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