In the figure /PX/ = /XQ/, PQ//YZ and XV//QR. What is the ratio of the area of XYZQ to te area of \(\bigtriangleup\)YZR?

In the figure /PX/ = /XQ/, PQ//YZ and XV//QR. What is the ratio of the area of XYZQ to te area of \(\bigtriangleup\)YZR?

A.

1:2

B.

2:1

C.

1:2

D.

3:1

Correct answer is B

From the diagram, XYZQ is a parallelogram. Thus, |YZ| = |XQ| = |PX|; \(\bigtriangleup\)PXY, Let the area of XYZQ = A1, the area of \(\bigtriangleup\)PXY

= Area of \(\bigtriangleup\)YZR = A2

Area of \(\bigtriangleup\)PQR = A = A1 + 2A2

But from similarity of triangles

\(\frac{\text{Area of PQR}}{\text{Area of PXY}} = (\frac{PQ}{PX})^2 = (\frac{QR}{XY})^2\)

\(\frac{A}{A_2} = (\frac{2}{1})^2 = \frac{2}{1}\)

A = 4A2 But, A = A1 + 2A

A1 = 4A2 - 2A2

A1 = 2A2

\(\frac{A_1}{A_2}\) = 2

A1:A2 = 2:1


Area of XYZQ:Area of \(\bigtriangleup\)YZR = 2:1