For triangle ABC with DE || BC, AD = (4x - 3), DB = (3x - 1), AE = (8x - 7) and EC = (5x - 3). The value of x is ____.

Question

Accepted Answer

1. 4x-3/3x-1 = 8x-7/5x-3. Cross-multiply: (4x-3)(5x-3) = (3x-1)(8x-7). LHS = 20x^2 -12x -15x +9 = 20x^2 -27x +9. RHS = 24x^2 -21x -8x +7 = 24x^2 -29x +7. So 20x^2-27x+9 = 24x^2-29x+7, 0 = 4x^2 -2x -2, 2x^2 - x - 1 = 0, (2x+1)(x-1)=0, x = 1 (positive).

For triangle ABC with DE || BC, AD = $(4 x - 3)$ , DB = $(3 x - 1)$ , AE = $(8 x - 7)$ and EC = $(5 x - 3)$ . The value of $x$ is ____.

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More Class 10 Basic Proportionality Theorem practice

For triangle ABC with DE || BC, AD = (4x−3), DB = (3x−1), AE = (8x−7) and EC = (5x−3). The value of x is ____.

Step-by-Step Solution

Master this chapter in 30 minutes a day.

More Class 10 Basic Proportionality Theorem practice

For triangle ABC with DE || BC, AD = $(4 x - 3)$ , DB = $(3 x - 1)$ , AE = $(8 x - 7)$ and EC = $(5 x - 3)$ . The value of $x$ is ____.