Question

An isosceles triangle has two sides of equal length, both measuring eight inches, and a base 'b'. The perimeter of the triangle is 15.7 inches, so the equation to solve is a+b=15.7. Recall that the sum of the two lengths of any two sides of a triangle must be greater than the length of the third side.

Which of the following ranges for 'b' makes sense for possible values in this scenario?

A) b>0 and b<7.7
B) b>0 and b<8
C) b>0 and b<15.7
D) b>0 and b<8.7

Answer 1

The range of values for 'b' in the given scenario is a) b > 0 and b < 7.7.

Step-by-step explanation:

An isosceles triangle has two sides of equal length, both measuring eight inches, and a base 'b'. The perimeter of the triangle is 15.7 inches, so the equation to solve is a+b=15.7. Recall that the sum of the two lengths of any two sides of a triangle must be greater than the length of the third side.

To solve for 'b', we substitute the given value for 'a' (which is 8) into the equation. So we have 8 + b = 15.7. Solving for 'b', we subtract 8 from both sides, giving us b = 7.7.

Therefore, the range of values for 'b' that makes sense in this scenario is b > 0 and b < 7.7. Hence, the correct answer is option A) b > 0 and b < 7.7.