Question

the triangle shown is isosceles. find the length of each side and the perimeter. each of the two congruent sides has length 13. the third side has length (type integers or decimals.) the perimeter of the triangle is (type an integer or a decimal.)

Explanation:

Step1: Set up equation for isosceles - triangle.

Since it's an isosceles triangle, either \(5x - 17=11\) or \(5x - 17 = 2x+1\).

Case 1: Solve \(5x - 17=11\)

Add 17 to both sides: \(5x=11 + 17\), so \(5x=28\), then \(x=\frac{28}{5}=5.6\).
The sides are \(11\), \(11\), and \(2\times5.6+1=11.2 + 1 = 12.2\).
The perimeter is \(11+11+12.2 = 34.2\).

Case 2: Solve \(5x - 17=2x + 1\)

Subtract \(2x\) from both sides: \(5x-2x-17=2x-2x + 1\), \(3x-17 = 1\).
Add 17 to both sides: \(3x=1 + 17\), \(3x=18\), \(x = 6\).
The sides are \(5\times6-17=30 - 17 = 13\), \(13\), and \(2\times6+1=12 + 1=13\).
The perimeter is \(13+13+13=39\).
Since the problem seems to imply integer - valued sides (from the way it asks for integer or decimal), we consider the second case.
The lengths of the sides are \(13\), \(13\), \(13\).

Answer:

The length of each side is \(13\) cm and the perimeter is \(39\) cm.