Question
The square and triangle below have equal parameters
Square:x-5
Triangle:12
What is the value of X? find the perimeter
Square:x-5
Triangle:12
What is the value of X? find the perimeter
Answers
Answer
How should I type that in
Answered by
GPT-4o mini
To find the value of \( x \) given that the perimeters of a square and a triangle are equal, we first need to determine the formulas for the perimeters of each shape.
1. **Perimeter of the Square**: The perimeter \( P \) of a square is given by:
\[
P_{\text{square}} = 4 \times \text{side length}
\]
If the side length of the square is \( x - 5 \), then:
\[
P_{\text{square}} = 4(x - 5)
\]
2. **Perimeter of the Triangle**: If the perimeter of the triangle is given as 12, we have:
\[
P_{\text{triangle}} = 12
\]
3. **Setting the Perimeters Equal**: Since the perimeters are equal, we can set them equal to each other:
\[
4(x - 5) = 12
\]
4. **Solving for \( x \)**:
\[
4(x - 5) = 12
\]
Divide both sides by 4:
\[
x - 5 = 3
\]
Adding 5 to both sides gives:
\[
x = 3 + 5 = 8
\]
5. **Finding the Perimeter**: Now that we have \( x = 8 \), we can find the perimeter of the square:
\[
P_{\text{square}} = 4(x - 5) = 4(8 - 5) = 4(3) = 12
\]
Thus, the value of \( x \) is \( \boxed{8} \), and the perimeter of both the square and triangle is \( \boxed{12} \).
1. **Perimeter of the Square**: The perimeter \( P \) of a square is given by:
\[
P_{\text{square}} = 4 \times \text{side length}
\]
If the side length of the square is \( x - 5 \), then:
\[
P_{\text{square}} = 4(x - 5)
\]
2. **Perimeter of the Triangle**: If the perimeter of the triangle is given as 12, we have:
\[
P_{\text{triangle}} = 12
\]
3. **Setting the Perimeters Equal**: Since the perimeters are equal, we can set them equal to each other:
\[
4(x - 5) = 12
\]
4. **Solving for \( x \)**:
\[
4(x - 5) = 12
\]
Divide both sides by 4:
\[
x - 5 = 3
\]
Adding 5 to both sides gives:
\[
x = 3 + 5 = 8
\]
5. **Finding the Perimeter**: Now that we have \( x = 8 \), we can find the perimeter of the square:
\[
P_{\text{square}} = 4(x - 5) = 4(8 - 5) = 4(3) = 12
\]
Thus, the value of \( x \) is \( \boxed{8} \), and the perimeter of both the square and triangle is \( \boxed{12} \).
Answered by
GPT-4o mini
If you want to present the solution clearly, you can format it step by step. Here’s how you might type it:
---
**Problem Statement:**
The perimeter of a square and a triangle are equal. The perimeter of the square is expressed as \( x - 5 \) and the perimeter of the triangle is 12. Find the value of \( x \) and calculate the perimeter.
**Solution:**
1. **Perimeter of the Square:**
\[
P_{\text{square}} = 4 \times \text{side length}
\]
Given side length:
\[
\text{side length} = x - 5
\]
Therefore:
\[
P_{\text{square}} = 4(x - 5)
\]
2. **Perimeter of the Triangle:**
\[
P_{\text{triangle}} = 12
\]
3. **Setting the Perimeters Equal:**
\[
4(x - 5) = 12
\]
4. **Solving for \( x \):**
\[
4(x - 5) = 12
\]
Divide both sides by 4:
\[
x - 5 = 3
\]
Adding 5 to both sides gives:
\[
x = 8
\]
5. **Finding the Perimeter:**
Substitute \( x \) back into the square's perimeter formula:
\[
P_{\text{square}} = 4(x - 5) = 4(8 - 5) = 4(3) = 12
\]
**Final Answer:**
The value of \( x \) is \( \boxed{8} \), and the perimeter of both the square and the triangle is \( \boxed{12} \).
---
This format provides clarity by clearly indicating each step in the problem-solving process. You can use the mathematical notations and formatting as shown if you're using a word processor that supports it, otherwise, straightforward text is also acceptable.
---
**Problem Statement:**
The perimeter of a square and a triangle are equal. The perimeter of the square is expressed as \( x - 5 \) and the perimeter of the triangle is 12. Find the value of \( x \) and calculate the perimeter.
**Solution:**
1. **Perimeter of the Square:**
\[
P_{\text{square}} = 4 \times \text{side length}
\]
Given side length:
\[
\text{side length} = x - 5
\]
Therefore:
\[
P_{\text{square}} = 4(x - 5)
\]
2. **Perimeter of the Triangle:**
\[
P_{\text{triangle}} = 12
\]
3. **Setting the Perimeters Equal:**
\[
4(x - 5) = 12
\]
4. **Solving for \( x \):**
\[
4(x - 5) = 12
\]
Divide both sides by 4:
\[
x - 5 = 3
\]
Adding 5 to both sides gives:
\[
x = 8
\]
5. **Finding the Perimeter:**
Substitute \( x \) back into the square's perimeter formula:
\[
P_{\text{square}} = 4(x - 5) = 4(8 - 5) = 4(3) = 12
\]
**Final Answer:**
The value of \( x \) is \( \boxed{8} \), and the perimeter of both the square and the triangle is \( \boxed{12} \).
---
This format provides clarity by clearly indicating each step in the problem-solving process. You can use the mathematical notations and formatting as shown if you're using a word processor that supports it, otherwise, straightforward text is also acceptable.