To determine the length of the base \( b \) of the isosceles triangle, we start with the given information and the equation that models it:
1. We are given that each of the two equal sides of the isosceles triangle is \( a \), and we know \( a = 6.3 \) centimeters.
2. The perimeter of the triangle is 15.7 centimeters.
3. The equation modeling the perimeter, given \( a \), is \( 2a + b = 15.7 \).
Now we substitute the given value of \( a \) into the equation:
[tex]\[ 2 \cdot 6.3 + b = 15.7 \][/tex]
This simplifies to:
[tex]\[ 12.6 + b = 15.7 \][/tex]
Next, solve for \( b \) by isolating it on one side of the equation. Subtract \( 12.6 \) from both sides of the equation:
[tex]\[ b = 15.7 - 12.6 \][/tex]
Performing the subtraction, we get:
[tex]\[ b = 3.1 \][/tex]
Therefore, the length of the base \( b \) of the isosceles triangle is 3.1 centimeters.
Thus, the equation that can be used to find the length of the base when one of the longer sides is known is:
[tex]\[ 2a + b = 15.7 \][/tex]
And upon substituting \( a = 6.3 \):
[tex]\[ b = 15.7 - 12.6 \][/tex]
