# math

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the perimeter of a triangle is 42 inches. three times the length of the longest side minus the length of the shortest side is 49 inches. the sum of the length of the longest side and twice the sum of both the other side lengths is 65 inches. find the side lengths

• math -

a = the length of the shortest side

b = the length of the middle side

c = the length of the longest side

P = the perimeter

The perimeter of a triangle is 42 inches.

P = a + b + c

a + b + c = 42 Subtract c to both sides

a + b + c - c = 42 - c

a + b = 42 - c

The sum of the length of the longest side and twice the sum of both the other side lengths is 65 inches.

c + 2 ( a + b ) = 65

c + 2 ( 42 - c ) = 65

c + 2 * 42 - 2 * c = 65

c + 84 - 2 c = 65

- c + 84 = 65 Add c to both sides

- c + 84 + c = 65 + c

84 = 65 + c Subtract 65 to both sides

84 - 65 = 65 + c - c

19 = c

c = 19 in

Three times the length of the longest side minus the length of the shortest side is 49 inches.

3 c - a = 49 Add a to both sides

3 c - a + a = 49 + a

3 c = 49 + a Subtract 49 to both sides

3 c - 49 = 49 + a - 49

3 c - 49 = a

a = 3 c - 49

a = 3 * 19 - 49

a = 57 - 49 = 8

a = 8 in

a + b + c = 42

8 + b + 19 = 42

27 + b = 42 Subtract 27 to both sides

27 + b - 27 = 42 - 27

b = 15 in

The side lengths:

a = 8 in

b = 15 in

c = 19 in

• math -

84 = 65 + c Subtract 65 to both sides

84 - 65 = 65 + c - 65

19 = c

c = 19 in

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