Looking for trustworthy answers? Westonci.ca is the ultimate Q&A platform where experts share their knowledge on various topics. Experience the convenience of finding accurate answers to your questions from knowledgeable professionals on our platform. Connect with a community of professionals ready to provide precise solutions to your questions quickly and accurately.
Sagot :
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].
### 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].
We appreciate your visit. Our platform is always here to offer accurate and reliable answers. Return anytime. Thank you for choosing our platform. We're dedicated to providing the best answers for all your questions. Visit us again. Get the answers you need at Westonci.ca. Stay informed with our latest expert advice.