A Triangle Has Sides With Lengths 8x+6 And 5x-5. Find The Missing Side Length If The Triangle Has A Perimeter Of 7x+13.

a triangle has sides with lengths 8x+6 and 5x-5. find the missing side length if the triangle has a perimeter of 7x+13.

Answer:

Step-by-step explanation:

Perimeter of a triangle = Side₁ + Side₂ + Side₃

Side₃: y

Given:

Perimeter: 7x + 13

Side₁: 8x + 6

Side₂: 5x - 5

Side₃: y

Equation:

7x + 13 = (8x + 6) + (5x - 5) + y

7x + 13 = (13x + 1) + y

y = 7x + 13 - (13x + 1)

y = 7x + 13 - 13x - 1

y = -6x + 12

The third side is - 6x + 12.

Check:

Perimeter = Side₁ + Side₂ + Side₃

7x + 13 = (8x + 6) + (5x-5) + (-6x + 12)

7x + 13 = 8x + 6 + 5x - 5 - 6x + 12

7x + 13 = 7x + 13 (True)

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