Certainly! Let's go through the steps to determine which equation can be used to find the length of the base [tex]\( b \)[/tex] of the isosceles triangle.
We are given the following information:
1. The perimeter of the isosceles triangle is 15.7 centimeters.
2. The triangle has two sides of equal length, denoted by [tex]\( a \)[/tex], and a base of length [tex]\( b \)[/tex].
3. The equation modeling this information is [tex]\( 2a + b = 15.7 \)[/tex].
4. One of the longer sides [tex]\( a \)[/tex] is 6.3 centimeters.
Now, let's substitute the given value of [tex]\( a \)[/tex] into the equation to solve for [tex]\( b \)[/tex].
Starting from the perimeter equation:
[tex]\[ 2a + b = 15.7 \][/tex]
Substitute [tex]\( a = 6.3 \)[/tex] into the equation:
[tex]\[ 2 \cdot 6.3 + b = 15.7 \][/tex]
Simplify the expression:
[tex]\[ 12.6 + b = 15.7 \][/tex]
Therefore, the equation that can be used to find the length of the base [tex]\( b \)[/tex] is:
[tex]\[ 12.6 + b = 15.7 \][/tex]
So, the correct equation is [tex]\( 12.6 + b = 15.7 \)[/tex].
Among the given options, the correct answer is:
[tex]\[
12.6 + b = 15.7
\][/tex]
