Sure, let's solve the problem step-by-step.
### Problem:
You are given a triangle with a perimeter of [tex]\( 4 \ \text{cm} \)[/tex]. Two sides of this triangle are each [tex]\( 1 \ \text{cm} \)[/tex]. We need to find the length of the third side.
### Step-by-Step Solution:
1. Understand the Perimeter of the Triangle:
The perimeter of a triangle is the sum of the lengths of all three sides. If the sides are [tex]\(a\)[/tex], [tex]\(b\)[/tex], and [tex]\(c\)[/tex], then:
[tex]\[
\text{Perimeter} = a + b + c
\][/tex]
Here, the given perimeter is [tex]\( 4 \ \text{cm} \)[/tex].
2. Substitute the Known Values:
Let the three sides of the triangle be [tex]\(a\)[/tex], [tex]\(b\)[/tex], and [tex]\(c\)[/tex].
- [tex]\(a = 1 \ \text{cm}\)[/tex]
- [tex]\(b = 1 \ \text{cm}\)[/tex]
- [tex]\(c\)[/tex] is the unknown side we need to find.
Given the perimeter:
[tex]\[
a + b + c = 4 \ \text{cm}
\][/tex]
3. Plug in the Given Side Lengths:
Substitute the known values of [tex]\(a\)[/tex] and [tex]\(b\)[/tex] into the equation:
[tex]\[
1 + 1 + c = 4
\][/tex]
4. Solve for [tex]\(c\)[/tex]:
Combine the known values:
[tex]\[
2 + c = 4
\][/tex]
Next, isolate [tex]\(c\)[/tex] by subtracting 2 from both sides:
[tex]\[
c = 4 - 2
\][/tex]
[tex]\[
c = 2
\][/tex]
5. Conclusion:
The length of the third side of the triangle is [tex]\( 2 \ \text{cm} \)[/tex].
### Verification
To ensure our solution is correct, let’s verify the perimeter with the obtained side lengths:
[tex]\[
1 + 1 + 2 = 4 \ \text{cm}
\][/tex]
The calculated perimeter matches the given perimeter, confirming that the solution is correct.
So, the length of the third side in your triangle is [tex]\( 2 \ \text{cm} \)[/tex].
