<h3>
Answer: 60 units</h3>
=====================================================
Explanation:
The similar red marks on the angles tell us those angles are congruent. So they are the same measure.
The sides opposite those congruent angles are the same length. This means AC = BC. This triangle is isosceles.
--------------
Solve for x
AC = BC
5x-8 = 2x+7 .... substitution
5x-8-2x = 7 ... subtract 2x from both sides
5x-2x = 7+8 ..... add 8 to both sides
3x = 15
x = 15/3 ... divide both sides by 3
x = 5
---------------
Use that x value to compute each side length
AB = 3x+11 = 3*5+11 = 15+11 = 26
BC = 2x+7 = 2*5+7 = 10+7 = 17
CA = 5x-8 = 5*5-8 = 25-8 = 17
Note how BC and CA are the same length (17 units). This helps confirm we have the right x value.
----------------
The last step is to add up all the side lengths to get the perimeter
perimeter of triangle = sum of all the sides
perimeter of triangle = side1 + side2 + side3
perimeter of triangle ABC = AB + BC + CA
perimeter of triangle ABC = 26 + 17 + 17
perimeter of triangle ABC = 60 units
and![\sqrt[n]{x^m} =x^ \frac{m}{n}](https://tex.z-dn.net/?f=%20%5Csqrt%5Bn%5D%7Bx%5Em%7D%20%3Dx%5E%20%5Cfrac%7Bm%7D%7Bn%7D%20)
![\sqrt{ \sqrt[3]{2} }= \sqrt{2^ \frac{1}{3} } =( 2^ \frac{1}{3})^ \frac{1}{2} =2^ \frac{1}{6}](https://tex.z-dn.net/?f=%20%5Csqrt%7B%20%5Csqrt%5B3%5D%7B2%7D%20%7D%3D%20%5Csqrt%7B2%5E%20%5Cfrac%7B1%7D%7B3%7D%20%7D%20%3D%28%202%5E%20%5Cfrac%7B1%7D%7B3%7D%29%5E%20%5Cfrac%7B1%7D%7B2%7D%20%3D2%5E%20%5Cfrac%7B1%7D%7B6%7D%20%20)
