The first side of a triangle measures 4 in. less than the second side, the third side is 3 in more than the first side, and the perimeter is 15 in. How long is the third side?
If s represents the length of the second side, which of the following represents the length of the third side?
OS-4
O 5+3
OS-1

5 2/3 inchesS-1

Step-by-step explanation:

(a) Let x represent the length of the first side. Then the second side is (x+4) and the third side is (x+3). The perimeter is ...

  x + (x+4) +(x+3) = 15

  3x = 8 . . . . collect terms, subtract 7

  x = 2 2/3 . . . . divide by 3

The third side is x+3 = 5 2/3 inches.

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(b) For this, we are told the second side is S, so we have ...

  S = (x+4)

  x = S -4 . . . . . subtract 4 to solve for x

Using this in our expression (in part (a)) for the third side, we have ...

  third side = (x +3) = (S -4) +3

  third side = S -1

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