The expression 17n+11 represents the perimeter of a triangle. The other two sides measure 4n+5 and 5n+6. A simplified expression

Question

The expression 17n + 11 signifies the perimeter of a triangle. The other two sides are 4n + 5 and 5n + 6. What simplified expression represents the measure of the third side?

Response:

(17n + 11) - (4n + 5 + 5n + 6) =

Step-by-step clarification:

one simply deducts the measurement of the known sides from the total perimeter

(17n + 11) - (4n + 5 + 5n + 6) =

8n

Response: 8n

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Clarification:

The two sides, 4n+5 and 5n+6, comprise terms 4n and 5n which total to 9n. We require 8n to add to this to achieve 17n. In simpler terms, 4n + 5n + 8n = 9n + 8n = 17n

That is the reason why the outcome is 8n. There are no additional terms because the "+5" and "+6" in the two given expressions (4n+5 and 5n+6) sum to 5+6 = 11, matching what we aim for in the perimeter expression 17n + 11

Side 1 = 4n + 5

Side 2 = 5n + 6

Side 3 = 8n

Perimeter = (side1) + (side2) + (side3)

Perimeter = (4n + 5) + (5n + 6) + (8n)

Perimeter = 4n + 5 + 5n + 6 + 8n

Perimeter = (4n + 5n + 8n) + (5 + 6)

Perimeter = 17n + 11

So this confirms we possess the correct expression for the third side that is missing.