Question

If in a triangle XYZ, P, Q are points on XY, XZ respectively such that XP = 2PY, XQ = 2QZ, then the ratio, area of $\Delta XPQ$ : area of $\Delta XYZ$ is

• A. $4:9$
• B. $2:3$
• C. $3:2$
• D. $9:4$

Answer 1

The correct option is A $4:9$

Given, $XP=2PY$, $XQ=2QZ$ and the included angle is equal. Hence the triangles $XPQ$ and $XYZ$ are similar with their sides in the ratio of $2:3$. Thus the ratio of areas of the triangles is $4:9$