SOLUTION: ABC is a right triangle with area 30. The hypotenuse AC =13 and AB =5. Pick a point D in the interior of the triangle. X is the distance from D to the side AB, Y is the distance fr

Algebra ->  Triangles -> SOLUTION: ABC is a right triangle with area 30. The hypotenuse AC =13 and AB =5. Pick a point D in the interior of the triangle. X is the distance from D to the side AB, Y is the distance fr      Log On


   

Question 1101135: ABC is a right triangle with area 30. The hypotenuse AC =13 and AB =5. Pick a point D in the interior of the triangle. X is the distance from D to the side AB, Y is the distance from D to the side AC, and Z is the distance from D to the side BC. Calculate 5X+13Y+12Z.
Answer by greenestamps(13209) About Me  (Show Source):
You can put this solution on YOUR website!

With the given information, the length of BC is 12.

Consider triangles ADB, BDC, and CDA.

The area of triangle ADB is %281%2F2%29%285%29%28x%29
The area of triangle BDC is %281%2F2%29%2812%29%28z%29
The area of triangle CDA is %281%2F2%29%2813%29%28y%29

The area of triangle ABC is the sum of the areas of those three triangles:

%285x%2F2%29%2B%2812z%2F2%29%2B%2813y%2F2%29+=+30
%285x%2B12z%2B13y%29%2F2+=+30
5x%2B13y%2B12z+=+60