Answer:
39 inches
Step-by-step explanation:
The perimeter of a triangle is the sum of its three side lengths.
To find the perimeter of the given triangle, we first need to determine the value of x.
The internal angles of the triangle are congruent, as indicated by the single arc. A triangle with congruent internal angles is an equilateral triangle. In an equilateral triangle, the side lengths are equal, so to find the value of x, we can set the expression for one of the sides equal to another and solve for x:
[tex]\begin{aligned}2x - 3 &= x + 5\\2x-3-x&=x+5-x\\x-3&=5\\x-3+3&=5+3\\x &= 8\end{aligned}[/tex]
Therefore, the value of x is x = 8.
Now, substitute the value of x into one of the side length expressions. Let's use (21 - x):
[tex](21-8)\; \textsf{in}=13\; \textsf{in}[/tex]
So, the side length of the equilateral triangle is 13 inches.
Given that the sides are equal in length, the perimeter is simply 3 times the length of one side:
[tex]\textsf{Perimeter}=3 \times 13\;\sf in\\\\ \textsf{Perimeter}= 39\; \sf in[/tex]
Therefore, the perimeter of the triangle is:
[tex]\huge\boxed{\boxed{39 \; \sf inches}}[/tex]
