Sorry, not a right triangle (Need to draw, Part 5)

Geometry Level 3

The lengths of the sides of a triangle are 10, 17 and 21. How long is the altitude of the triangle to longest side?


The answer is 8.

Benedict Dimacutac by Benedict Dimacutac , 21, Philippines

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1 solution

Achal Jain
Jan 29, 2016

The easiest solution would be to find the area of the triangle by heron's formula which would come out to be 84. Then we can put it into the equation 1/2* 21* altitude= 84

1 Helpful 0 Interesting 0 Brilliant 0 Confused

Another approach would be to note that the triangle with the given sides can be formed by placing a 6 / 8 / 10 6/8/10 right triangle back-to-back (along the side length 8 8 ) with an 8 / 15 / 17 8/15/17 right triangle. (The respective sides lengths 6 6 and 15 15 would be collinear, forming the length 21 21 side of the given triangle.)

Brian Charlesworth - 5 years, 4 months ago

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