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In triangle ABC, DE || BC. If AD = $(x + 3)$ , DB = $(3 x + 19)$ , AE = $x$ and EC = $(3 x + 4)$ , find the value of $x$ .

Class 10Basic Proportionality TheoremGeometry — Similarity

A2
B3
C4
D5

Step-by-Step Solution

\frac{x + 3}{3 x + 19} = \frac{x}{3 x + 4}

. Cross:

(x + 3) (3 x + 4) = x (3 x + 19), 3 x^{2} + 13 x + 12 = 3 x^{2} + 19 x, 12 = 6 x, x = 2

.

Answer: A) 2

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