The lengths that make the sense for the value of b are 0.5 inches and 2 inches.
<h2>Given </h2>An isosceles triangle has two sides of equal length, a, and a base, b.
The perimeter of the triangle is 15.7 inches, so the equation to solve is 2a + b = 15.7.
<h3>What is the triangle inequality theorem?</h3>If two sides of a triangle are unequal, the longer side has a greater angle opposite to it.
The equation of the perimeter of the triangle;
1. Substitute b = 0.5 in the equation;
Then,
Verify the triangle inequality theorem;
0.5 + 7.6 > 7.6 is true
7.6 + 7.6 > 0.5 is true
2. Substitute b = 2 in the equation;
Then,
Verify the triangle inequality theorem;
0.5 + 76.85 > 6.85 is true
6.85 + 6.85 > 2 is true
Hence, the lengths that make the sense for the value of b are 0.5 inches and 2 inches.
To know more about the Triangle inequality theorem click the link given below.