in triangle STU, V is a point on the side ST and W is a point on the side SU such that VWUT is a trapezium. Given that VW : TU= 2 : 7, what is the ratio of area of trapezium VWUT to the area of the triangle STU?
Show answer & explanation
Correct answer: C
Explanation
The correct answer is option 3 i.e. 45:49.
VW : TU = 2 : 7
The ratio of the areas of two similar triangles is the square of the ratio of their corresponding sides.
So, Area(ΔSVW)/Area(ΔSTU) = (2/7)2 = 4/49
Let Area(ΔSTU) = 49x and Area(ΔSVW) = 4x
Area of Trapezium VWUT = Area(ΔSTU) - Area(ΔSVW) = 49x - 4x = 45x
(Area of Trapezium VWUT)/Area(ΔSTU) = 45x/49x = 45/49
Therefore, the ratio of the area of trapezium VWUT to the area of triangle STU is 45 : 49.