SOLUTION: The sides of a triangle are 9 cm , 12 cm and 15 cm. Find the length of the perpendicular drawn to the side whose length is 15 cm

Question 636470: The sides of a triangle are 9 cm , 12 cm and 15 cm. Find the length of the perpendicular drawn to the side whose length is 15 cm
Answer by DrBeeee(684) (Show Source): You can put this solution on YOUR website!
If 15^2 = 9^2 +12^2, the triangle satisfies the Pythagorean Theorem for a right triangle.
Is (15^2 = 81 + 144)?
Is (225 = 225)? Yes
Therefore the given triangle is a right triangle. Let the vertex of the right angle be C, the leg AC is 12, the hypotenuse AB is 15 and the leg BC is 9. The line perpendicular to the hypotenuse at a point D that connects to the vertex C is the "height" of the triangle ABC. It can be shown that the three angles of the triangle ABC are equal to those of triangle CBD. Thus triangle ABC is similar to CBD. The problem is to find the lenght of the line CD.
Using proportions of corresponding sides we have
CD/9 = 12/15
CD = 9*12/15
CD = 36/5
Answer: the line is 7.2 cm.
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