SOLUTION: the perimeter of an equilateral triangle is 32 centimeters. find the length of an altitude of the triangleto the nearest tenth of a centimeter.

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Question 409590: the perimeter of an equilateral triangle is 32 centimeters. find the length of an altitude of the triangleto the nearest tenth of a centimeter.
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!

the perimeter of an equilateral triangle P+=+3a, so

32cm=+3a.solve for a
32cm%2F3=+a
10.67cm=+a

find the length of an altitude h of the triangle
imagine, you drop the vertical+bisector from the top angle down to the bottom side in your triangle
note that this bisector is also the altitude (height) of the triangle which equilateral triangle split in half (two right triangles)

so, by using the Pythagorean Theorem, we get that the length of the altitude
h%5E2=a%5E2-%28a%2F2%29%5E2.........plug in 10.67cm=+a
h%5E2=%2810.67cm%29%5E2-%28%2810.67cm%29%2F2%29%5E2
h%5E2=%2810.67cm%29%5E2-%285.335cm%29%5E2
h%5E2=113.85cm%5E2-+28.46cm%5E2
h%5E2=85.39cm%5E2
h=sqrt%2885.39cm%5E2%29
h=9.2406709713093886351353067060983cm%29
h=9.2cm%29