Find the value of x for which DE || AB in given figure.
Given,
DE || AB
∴ If a line is drawn parallel to one side of a triangle to intersect the other sides in distinct points, the other two sides are divided in the same ratio.
So, the line drawn is equals to the third side of the triangle.
⇒ (x + 3) (3x + 4) = x (3x + 19)
⇒ 3x2 + 4x + 9x + 12 = 3x2 + 19x
⇒ 19x - 13x = 12
⇒ 6x = 12
∴ x = 12/6 = 2
[By basic proportionality theorem]
Hence, the required value of x is 2.
2