The side lengths in yards of a triangle and a square are shown in the diagram.
 


The perimeter of the triangle is equal to the perimeter of the square. 

What is the value of x?
A.−4

B.6

C.23

D.52

Let’s break down the problem step by step:

### 1. Triangle's Perimeter:
The perimeter of a triangle is the sum of its three side lengths. Based on the information given, let's denote the sides of the triangle as:

- \( a \)
- \( b \)
- \( c \)

Thus, the perimeter of the triangle is:
\[
P_{\text{triangle}} = a + b + c
\]

### 2. Square's Perimeter:
The perimeter of a square is four times the length of one of its sides, since all sides are equal. If the side length of the square is \( x \), then the perimeter of the square is:
\[
P_{\text{square}} = 4x
\]

### 3. Perimeter Equality:
According to the problem, the perimeter of the triangle is equal to the perimeter of the square. Therefore, we can set up the equation:
\[
a + b + c = 4x
\]

### 4. Solving for \( x \):
At this point, I would need the actual side lengths of the triangle from the diagram to proceed with solving the equation. If you could provide those, I can plug them into the equation and find the value of \( x \).

Feel free to upload the diagram or provide the missing side lengths, and I’ll continue from there.

Would you like to proceed with this, or do you have other questions? Here are 5 related questions:

1. How do you find the perimeter of other polygons like pentagons or hexagons?
2. How does changing one side of a triangle affect its perimeter?
3. How do you solve for unknowns in perimeter equations involving multiple shapes?
4. What are the properties of a triangle and square in relation to their perimeter?
5. How do you find the area of a square when you know its perimeter?

**Tip**: For shapes like squares and triangles, the perimeter formula helps you relate the side lengths and solve for unknowns efficiently!

The side lengths in yards of a triangle and a square are shown in the diagram. The perimeter of the triangle is equal to the perimeter of the square. What is the value of x?
A.−4
B.6
C.23
D.52

In this problem, the perimeter of a triangle is equal to the perimeter of a square. Learn how to solve for x by setting up equations based on the perimeter formulas for both shapes. Suitable for students in Grades 6-8.

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