Question

In the figure, XP is the bisector of angle X. What is the ratio of areas of Triangle YPX and triangle ZPX??
Pls explain....​

Answer 1

Answer:

XP is angle bisector of X

therefore by angle bisector theorem

$\frac{xy}{ xz} = \frac{yp}{pz}$

Angle YXP=Angle PXZ

by SAS similarity

triangle YPX is similar to triangle ZPX

then

$\frac{area \: of \: triangle \: yxp}{area \: of \: triangle \: pxz} = \frac{6}{4}$