Question

The perimeter of a triangle is

17
x
−
5
units. One side is
3
x
+
5
units and another is
8
x
−
3
units. How many units long is the third side?

Answer 1

`Side\ 3 = 6x - 7`

Explanation:

Given

`Perimeter = 17x - 5`

`Side\ 1 = 3x + 5`

`Side\ 2 = 8x - 3`

Required

Determine the length of the third side

The perimeter of a triangle is calculated as thus:

`Perimeter = Side\ 1 + Side\ 2 + Side\ 3`

Substitute values for Perimeter, Side 1 and Side 2

`17x - 5 = 3x + 5 + 8x - 3 + Side\ 3`

Collect Like Terms

`17x - 5 = 3x + 8x + 5 - 3 + Side\ 3`

`17x - 5 = 11x + 2 + Side\ 3`

Solve for Side 3

`Side\ 3 = 17x - 11x - 5 - 2`

`Side\ 3 = 6x - 7`

Hence, the length of the third side is 6x - 7 units