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

Answer:

$Side\ 3 = 6x - 7$

Step-by-step 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