The third side of the triangle is 6x−7 units long
From the question,
The perimeter of a triangle is 17x−5 units.
Let P represent the perimeter of the triangle.
∴ P = 17x−5 units
Also, let the sides of the triangle be a, b and c.
From the question, one side is 3x+5 units, let this side be a
∴ a = 3x+5 units
and another is 8x−3 units, let this side be b
∴ b = 8x−3 units
Now, to determine how many units long the third side is,
Let the third side be c
The formula for calculating the perimeter of a triangle is given as
P = a + b + c
Put the values above into the equation,
∴ 17x−5 = 3x+5 + 8x−3 + c
Now, we will determine the value of c
First, simplify collect like terms
We get
17x − 3x − 8x = 5 + 5 −3 + c
Now, simplify further
6x = 7 + c
Then,
6x − 7 = c
∴ c = 6x − 7
Hence, the third side of the triangle is 6x−7 units long
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