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By setting up proportion using known side lengths and the missing variable in the ratio of the similar triangles ABC and ADEF, we can cross-multiply and solve for 'x' which ends up being approximately 4.17.
Given that triangles ABC and ADEF are similar, we can set up a proportion, specifically, the ratio of the corresponding sides would be equal. By looking at the provided figure, we can set up a proportion leveraging the given sides lengths of 35, 5, and 42, and the unknown 'x'.
We set the proportion as following: AB/AD = BC/EF which results in 35/42 = x/5.
Solving this proportion for x is our goal and we simply cross multiply the fractions to get 35*5 = 42*x which results in 175 = 42x. Then dividing both sides by 42, we get x = 175/42. And simplification of this fraction results in approximately 4.17
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