Sure, let's walk through the problem step by step.
1. Identify the given information:
- The perimeter of the isosceles triangle is \( 15.7 \) centimeters.
- The lengths of the two equal sides (\( a \)) are each \( 6.3 \) centimeters.
2. Understand the problem:
- An isosceles triangle has two sides of equal length.
- The perimeter of a triangle is the sum of the lengths of all its sides.
3. Set up the equation for the perimeter:
- The sides are: two sides of length \( a \) and one side of length \( b \).
- The equation for the perimeter \( P \) of an isosceles triangle is:
[tex]\[
P = 2a + b
\][/tex]
- Substituting the given values into the equation, where \( P = 15.7 \) cm and \( a = 6.3 \) cm, we get:
[tex]\[
15.7 = 2(6.3) + b
\][/tex]
4. Substitute the value of \( a \):
- Substitute \( a = 6.3 \) into the equation:
[tex]\[
15.7 = 2(6.3) + b
\][/tex]
- Simplify the equation:
[tex]\[
15.7 = 12.6 + b
\][/tex]
5. Solve for \( b \):
- Isolate \( b \) by subtracting \( 12.6 \) from both sides of the equation:
[tex]\[
b = 15.7 - 12.6
\][/tex]
- Calculate the result:
[tex]\[
b = 3.1
\][/tex]
Therefore, the length of the base \( b \) is approximately \( 3.1 \) centimeters.
The equation used to find the length of the base \( b \) is:
[tex]\[
b = 15.7 - 12.6
\][/tex]
Hence, the length of the base [tex]\( b \)[/tex] is [tex]\( 3.1 \)[/tex] centimeters.
