Question : 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 the area of trapezium VWUT to the area of the triangle STU?
Option 1: 4 : 49
Option 2: 4 : 45
Option 3: 45 : 49
Option 4: 49 : 81
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Correct Answer: 45 : 49
Solution :
Given,
In
So,
We know, that the ratio of the area of similar triangles is equal to the ratio of the squares of corresponding sides of similar triangles.
So,
⇒
Now,
⇒
⇒
⇒
Hence, the correct answer is 45 : 49.
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