To find the length of the base [tex]\( b \)[/tex] of the isosceles triangle, we start with the information given in the problem:
1. The perimeter of the triangle is 15.7 centimeters.
2. The triangle has two longer sides (each [tex]\( a \)[/tex]), and one base ([tex]\( b \)[/tex]).
3. One of the longer sides ([tex]\( a \)[/tex]) is 6.3 centimeters.
Using the given perimeter, the relation between the sides can be expressed as:
[tex]\[ 2a + b = 15.7 \][/tex]
Given that [tex]\( a = 6.3 \)[/tex] centimeters, we can substitute [tex]\( a \)[/tex] into the equation:
[tex]\[ 2(6.3) + b = 15.7 \][/tex]
Now, simplify the equation:
[tex]\[ 12.6 + b = 15.7 \][/tex]
To isolate [tex]\( b \)[/tex], subtract 12.6 from both sides:
[tex]\[ b = 15.7 - 12.6 \][/tex]
Finally, after performing the subtraction, we get:
[tex]\[ b = 3.1 \][/tex]
Therefore, the equation that can be used to find the length of the base [tex]\( b \)[/tex] is:
[tex]\[ b = 15.7 - 2(6.3) \][/tex]
From the calculations, the length of the base [tex]\( b \)[/tex] is 3.1 centimeters.
