Question

In an Triangle if AX = a , XB =B, AY= X , YC= Y then a+b/ a =​

Answer 1

$In \: \triangle ABC , XY\parallel BC, and$

$AX = b , XB = b , AY = x \:and \: YC = y$

__________________

/* By Basic Proportionality Theorem */

If a line is drawn parallel to one side of a triangle to intersect the other two sides in distinct points , then the other two sides are divided in the same ratio .

________________

$Here, In \:\triangle ABC, XY\parallel BC$

$\frac{XB}{AX} = \frac{YC}{AY}$

$\implies \frac{XB}{AX} + 1 = \frac{YC}{AY} + 1$

$\implies \frac{b}{a} + 1 = \frac{y}{x} + 1$

$\implies \frac{b+a}{a} = \frac{y+x}{x}$

$\therefore \red{ \frac{a+b}{a} }\green{= \frac{x+y}{x}}$

•••♪