Question

Mark the correct choice as.
Assertion (A): In △ABC, DE || BC such that AD = (7x − 4) cm, AE = (5x − 2) cm, DB = (3x + 4) cm, and EC = 3x cm then x equal to 5.

Reason (R): If a line is drawn parallel to one side of a triangle intersecting the other two sides in distinct points, then the other two sides are divided in the same ratio.

• A. Both A and R are true, and R is not the correct explanation of A.
• B. Both A and R are true, and R is the correct explanation of A.
• C. A is false but R is true.
• D. A is true but R is false.

Answer 1

The correct option is C A is false but R is true.

In △ABC, DE || BC such that AD = (7x − 4) cm, AE = (5x − 2) cm, DB = (3x + 4) cm, and EC = 3x cm
By applying BPT, we get,

$\frac{AD}{DB}$ = $\frac{AE}{EC}$

$\frac{7x-4}{3x+4}$ = $\frac{5x-2}{3x}$

$(7x-4)\left(3x\right)=(5x-2)(3x+4)$

$6x^2-26x+8=0$

$x=4or\frac{1}{3}$

Hence, A is incorrect but R is correct.