Question

0.33. In figure the line comentXY is parallel to side AC Of A ABC and it divides the talen
to two parts of equal areas. Find the ratio AX/AB​

Answer 1

Correct question

In the given figure, line segment XY is parallel to side AC of triangle ABC and it divides the triangle into two parts of equal area. Prove that AX : AB = √2 -1 / √2

Answer

To solve: 2 Area (xy) = Area (ABC)

In ΔABC & ΔXBY

∠ABC=∠XBY(common)

∠ACB=∠XYB (since XY||AC, angles are equal)

ΔABC∼ΔXBY (AA similarity)

(AB/XB)^2 = Area(ΔABC)/Area(ΔBXY) = 2

=> (AB)^2=2(XB)^2=_/2×B

=> AX=AB−XB=AB/_/2 = _/2 - 1/ _/ 2

=>AX/AB = _/2- 1/_/2.