You need geometric means formulas for right triangles here in order to solve this. Unfortunately, since we don't have letters to mark our divisions on the triangle we will have to use the names of the cities and highway as our variables in our proportions. The first one will look like this: [tex] \frac{BlareToAltitude}{BlareToCray}=\frac{BlareToCray}{highway} [/tex]. Filling that in accordingly, we have [tex] \frac{13-a}{5}=\frac{5}{13} [/tex]. We will cross multiply to solve for a which is the distance from Blare to the altitude. 25=13(13-a) and 25=169-13a. -144 = -13a so a the distance from Blare to the altitude is about 11.08. That means that the distance from Alba to the altitude is 13-11.08 which is 1.92. Now that we know the side length and the 2 distances that make up the hypotenuse of that large right triangle, we can solve for x, the altitude. Using the geometric mean that solves for this is this formula: [tex] \frac{BlareToAltitude}{x}=\frac{x}{AlbaToAltitude} [/tex]. Again we cross multiply to get [tex] x^2=21.2736 [/tex]. When we take the square root of 21.2736 we get that x = 4.6. So your answer is the second choice down.
