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):
You can put this solution on YOUR website!
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.

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Good luck in your studies!

Respectfully,
Dr J