In the figure /PX/ = /XQ/, PQ//YZ and XV//QR. What is the ratio of the area of XYZQ to te area of △YZR?
1:2
2:1
1:2
3:1
Correct answer is B
From the diagram, XYZQ is a parallelogram. Thus, |YZ| = |XQ| = |PX|; △PXY, Let the area of XYZQ = A1, the area of △PXY
= Area of △YZR = A2
Area of △PQR = A = A1 + 2A2
But from similarity of triangles
Area of PQRArea of PXY=(PQPX)2=(QRXY)2
AA2=(21)2=21
A = 4A2 But, A = A1 + 2A
A1 = 4A2 - 2A2
A1 = 2A2
A1A2 = 2
A1:A2 = 2:1
Area of XYZQ:Area of △YZR = 2:1
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