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: Option B
Explanation
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