The expression 17n + 11 represents the perimeter (in feet) of the triangle. Write an expression that represents the measure of the third side. On either side of the triangle, there are two expressions, one being 5n + 6 and 4n + 5.
The answer is 8n, I don't know how to explain. I kind of figured it out in my head somehow.
perimeter-side1-side2=third side
17n+11-(5n+6) -(4n+5)= third side
To find the expression that represents the measure of the third side of the triangle, we need to subtract the sum of the other two side lengths from the perimeter.
The sum of the other two side lengths is (5n + 6) + (4n + 5). Simplifying this expression, we have 5n + 6 + 4n + 5.
Adding the terms with 'n' together, we get 5n + 4n = 9n. And adding the constant terms together, we have 6 + 5 = 11.
So the sum of the other two side lengths is 9n + 11.
To find the expression that represents the measure of the third side, we subtract this sum from the given perimeter of the triangle: 17n + 11 - (9n + 11).
Simplifying this expression, we get 17n + 11 - 9n - 11.
Combining like terms, 17n - 9n is equal to 8n, and 11 - 11 equals 0.
Therefore, the expression that represents the measure of the third side of the triangle is 8n.