SOLUTION: the perimeter of an equilateral triangle is 21 inches. find the length of the altitude.

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Question 215348: the perimeter of an equilateral triangle is 21 inches. find the length of the altitude.
Answer by drj(1380) About Me  (Show Source):
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The perimeter of an equilateral triangle is 21 inches. find the length of the altitude.

Step 1. An equilateral triangle has three equal sides. Let c be the side.

Step 2. Perimeter P means adding up the three sides of the triangle or P=c+c+c=3c

Step 3. Then c=P%2F3=21%2F3=7

Step 4. The altitude a is one of the sides of a right triangle inside the equilateral triangle while the other leg is b=c%2F2=7%2F2=3.5 inches.

Step 5. The Pythagorean theorem states that the sum of the squares of the legs a%5E2%2Bb%5E2is equal to the square of the hypotenuse c%5E2 or

c%5E2=a%5E2%2Bb%5E2

7%5E2=a%5E2%2B3.5%5E2

a%5E2=49-12%2F25

a=sqrt%2836.75%29

a=6.06 inches

Step 5. ANSWER: Altitude is 6.06 inches.

I hope the above steps were helpful.

For FREE Step-By-Step videos in Introduction to Algebra, please visit http://www.FreedomUniversity.TV/courses/IntroAlgebra and for Trigonometry visit http://www.FreedomUniversity.TV/courses/Trigonometry.

Good luck in your studies!

Respectfully,
Dr J