In triangle ABC, the point D lies on AB and the point E lies on AC, with DE parallel to BC. If AD = x, DB = x − 2, AE = x + 2 and EC = x − 1, what is the value of x?

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4. Since DE ∥ BC, the basic proportionality theorem gives AD/DB = AE/EC, so x/(x − 2) = (x + 2)/(x − 1). Cross-multiplying, x(x − 1) = (x + 2)(x − 2), that is x² − x = x² − 4, so x = 4. Check: AD = 4, DB = 2, AE = 6, EC = 3, and 4/2 = 6/3 = 2.

In triangle ABC, the point D lies on AB and the point E lies on AC, with DE parallel to BC. If AD = $x$ , DB = $x - 2$ , AE = $x + 2$ and EC = $x - 1$ , what is the value of $x$ ?

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In triangle ABC, the point D lies on AB and the point E lies on AC, with DE parallel to BC. If AD = x, DB = x−2, AE = x+2 and EC = x−1, what is the value of x?

Step-by-Step Solution

Master this topic in 30 minutes a day.

More Geometry practice

In triangle ABC, the point D lies on AB and the point E lies on AC, with DE parallel to BC. If AD = $x$ , DB = $x - 2$ , AE = $x + 2$ and EC = $x - 1$ , what is the value of $x$ ?