Question

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. If we recall that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side, which lengths make sense for possible values of b? Select two options

Answer 1

To find the possible values of b in the equation 2a + b = 15.7 in an isosceles triangle, we can assume different values for a and solve for b. Two lengths that make sense for possible values of b are 5.7 and 3.7.

Step-by-step explanation:

To determine which lengths make sense for possible values of b in the equation 2a + b = 15.7, we need to consider the fact that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side. Since the triangle is isosceles, two sides have the same length, which is represented by a. Let's assume that a = 5 (one possible value) and substitute it into the equation: 2(5) + b = 15.7. Solving for b, we get b = 5.7. This means that a possible value for b is 5.7. Another option is when a = 6, which gives us b = 3.7. Therefore, the two lengths that make sense for possible values of b are 5.7 and 3.7.