In 𝛥 ABC, DE ‖ AB. If AB = a, DE = x, BE = b and EC = c.Then x expressed in terms of a, b and c is:
Question
In 𝛥 ABC, DE ‖ AB. If AB = a, DE = x, BE = b and EC = c. Then x expressed in terms of a, b and c is:
Solution
This problem can be solved using the properties of similar triangles.
Since DE is parallel to AB, we can say that triangle DEC is similar to triangle BAC by the AA (Angle-Angle) criterion of similarity.
In similar triangles, the ratio of corresponding sides is equal. Therefore, we can write:
DE/AB = EC/AC = BC/BC
Substituting the given values, we get:
x/a = c/(b+c)
To express x in terms of a, b, and c, we can rearrange this equation to solve for x:
x = a * c / (b + c)
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