In triangle ABC, X and Y are the points on sides AB and AC, respectively, such that XY is parallel to BC. If XY : BC = 2.5 : 7, what is the ratio of the area of the trapezium BCYX to that of the ΔAXY?
Answer & explanation
Correct answer: option 4
The ratio of XY : BC = 2.5 : 7 = 5 : 14
Now the areas = Square of the sides
\(\frac{arAXY}{arABC}\) = \(\frac{5^2}{14^2}\)
\(\frac{arAXY}{arABC}\) = \(\frac{25}{196}\)
Now the area of trapezium XYBC = 196 - 25 = 171
So, the ratio of the area of the trapezium BCYX to that of the ΔAXY = $\frac{171}{25}$