# Perimeter of a triangle

Given sides a, b, and c, finding the perimeter of a triangle is given by the following formula:

Start with a scalene triangle and label the sides as shown below.
P = a + b + c

Find the perimeter of a triangle when a = 3 cm, b = 5 cm, and c = 7

P = 3 + 5 + 7 = 15 cm

Find the perimeter when a = 4 cm, b = 8 cm, and c = 12

P = 4 + 8 + 12 = 24 cm

Find the perimeter when a = 1/2 cm, b = 3/2 cm, and c = 6/2

P = 1/2 + 3/2 + 6/2 = ( 1 + 3 + 6)/2 = 10/2 = 5 cm

If P = 30 cm and a = 5 and b = 7, what is c?

Using the formula P = a + b + c, replace everything you know or everything given to you into the formula

Things that are given are P = 30, a = 8, and b = 10

Replacing them into the formula gives:

30 = 8 + 10 + c

30 = 18 + c

You end up with an addition equation that you can solve to get c

However, some mental math should provide you with an answer too.

Replace c by a question mark (?) and say to yourself the following:

18 + ? = 30 or what can I add to 18 to get 30 ? 18 + 12 = 30, so c = 12

If P = 20 cm, b = 7 and c = 8, what is a?

Using the formula P = a + b + c, replace everything you know or everything given to you into the formula

Things that are given are P = 20, b = 7, and c = 8

Replacing them into the formula gives:

20 = a + 7 + 8

20 = a + 15

What can I add to 15 to get 20? The answer is 5, so a = 5

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