NIELIT 2019 Feb Scientist C - Section D: 6

Question

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

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

Answer 1

Correct option is A)

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