The figure to the right shows a triangle with three cevians drawn through an interior point, and all perimeter segment lengths are given in meters. What is the value of s?
I'm not sure if there is any significance in all three ceva meeting at one point within the triangle... I feel like there might be, but I don't see how to utilise this fact.
I thought using heron's formula and then comparing it to another way of getting the triangle's area. However, I'm not sure how I can get the triangle's area the second (unknown) way.
Perhaps I could use triangle inequality, but that doesn't seem to get me very far, either.
How can I solve this?
Do you know Ceva's theorem? Acording to that theorem we have:
$${s\over 5}\cdot {4\over 3}\cdot {4\over 2}=1$$
so...