The first side of a triangle is 4 inches shorter than the second side. The third side is 10 inches longer than the second side. The perimiter of the triangle is 66 inches, how long is each side?

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Step-by-step explanation:

11, 7, 17 sides

Step-by-step explanation:

LABELS: x = base, x-4 = one side, x+6 = second side. Perimeter = a + b + c.

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VERBAL MODEL - the sum of the three sides must be greater than or equal to 26.

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ALGEBRAIC MODEL - x + x-4+x+6 >= 26

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SOLVE:

x+%2B+x-4%2Bx%2B6+%3E=+26

combine like terms to get

3x%2B2+%3E=26

subtract to get

3x+%3E=24

divide to get

x+%3E=8

So,

x = 8,

x-4 = 4

x+6 = 14

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However, these side length don't make a triangle. The first base value that does work is 11.

x = 11

x-4 = 7

x+6 = 17

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CHECK

4+8+14 >= 26

16>= 26 [true].

However, these side length don't make a triangle.

11+7+17 >= 26

35>= 26 [true]