SOLUTION: A triangle has a 3-inch side, a 4-inch side, and a 5-inch side. The altitude drawn to the 5-inch side cuts this side into segments of what lengths?

Question 1139377: A triangle has a 3-inch side, a 4-inch side, and a 5-inch side. The altitude drawn to the 5-inch side cuts this side into segments of what lengths?
Answer by greenestamps(13198) (Show Source): You can put this solution on YOUR website!

The given triangle, with side lengths 3, 4, and 5, is a right triangle.

Let the triangle be ABC, with the right angle at C; AC=3, BC=4; AB=5. The altitude to the hypotenuse, CD, divides triangle ABC into two smaller right triangles that are both similar to triangle ABC. You can find the lengths of AD and BD using those similar triangles.

Using the similar triangles ADC and ABD,

Then of course BD is 5-1.8=3.2; but you could also find that using similar triangles CDB and ACB:

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