In triangle ABC, DE || BC. AD = x, DB = x - 2, AE = x + 2 and EC = x - 1, find the value x.

Expert Solution

In △ABC, we have DE || BC

Therefore

From Thales theorem, we know that the ratio of any two corresponding sides in two equiangular triangles is always the same. This theorem is called as Basic Proportionality Theorem

AD /DB = AE/ EC

AD × EC = AE × DB

On substituting the known values we get

x(x-1) = (x-2)(x+2)

x2 – x = x2 – 4

-x=-4

x = 4

The value of x =4.

Nikhil Thakur answered 2 years ago

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