To solve this problem, let's break it down step by step.
First, we need to understand what we are given:
1. This is an isosceles triangle, which means it has two sides of equal length.
2. The lengths of these two equal sides are denoted by [tex]\( a \)[/tex].
3. The base, which is the third side of the triangle, is denoted by [tex]\( b \)[/tex].
4. The perimeter of the triangle is given as 15.7 centimeters.
From the problem, we are also given the equation that represents the perimeter of the triangle:
[tex]\[ 2a + b = 15.7 \][/tex]
We are provided with the length of one of the equal sides:
[tex]\[ a = 6.3 \][/tex]
To find the equation that models the base [tex]\( b \)[/tex], we substitute the given value of [tex]\( a \)[/tex] into the perimeter equation:
1. Start with the original equation:
[tex]\[ 2a + b = 15.7 \][/tex]
2. Substitute [tex]\( a = 6.3 \)[/tex] into the equation:
[tex]\[ 2(6.3) + b = 15.7 \][/tex]
3. Simplify [tex]\( 2 \times 6.3 \)[/tex]:
[tex]\[ 12.6 + b = 15.7 \][/tex]
4. To isolate [tex]\( b \)[/tex], subtract 12.6 from both sides of the equation:
[tex]\[ b = 15.7 - 12.6 \][/tex]
5. Perform the subtraction:
[tex]\[ b = 3.1 \][/tex]
Thus, the equation that can be used to find the length of the base [tex]\( b \)[/tex] after substituting [tex]\( a \)[/tex] is:
[tex]\[ b = 15.7 - 2a \][/tex]
This equation correctly reflects the length of the base when [tex]\( a = 6.3 \)[/tex].
