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

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(13216) (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
The area of triangle BDC is
The area of triangle CDA is

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

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