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This isosceles triangle has two sides of equal length, [tex]a[/tex], that are longer than the length of the base, [tex]b[/tex]. The perimeter of the triangle is 15.7 centimeters. The equation [tex]2a + b = 15.7[/tex] models this information. If one of the longer sides is 6.3 centimeters, which equation can be used to find the length of the base?

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GinnyAnsweridn
Certainly! Let's solve the problem step-by-step.

1. We know that the perimeter of the isosceles triangle is given by the equation:
[tex]\[ 2a + b = 15.7 \][/tex]

2. We are also informed that each of the two equal sides, [tex]\(a\)[/tex], is 6.3 centimeters. So we can substitute [tex]\(a = 6.3\)[/tex] into the equation.

3. Substituting [tex]\(a = 6.3\)[/tex] into the perimeter equation, we get:
[tex]\[ 2(6.3) + b = 15.7 \][/tex]

4. Simplify [tex]\(2(6.3)\)[/tex] to get:
[tex]\[ 12.6 + b = 15.7 \][/tex]

5. To find [tex]\(b\)[/tex], we need to isolate it by subtracting 12.6 from both sides of the equation:
[tex]\[ b = 15.7 - 12.6 \][/tex]

6. Performing the subtraction gives:
[tex]\[ b = 3.1 \][/tex]

Hence, the length of the base, [tex]\(b\)[/tex], is 3.1 centimeters. The equation used to find the length of the base [tex]\(b\)[/tex] was [tex]\(b = 15.7 - 12.6\)[/tex].
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