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. –2 in. 0 in. 0. 5 in. 2 in. 7. 9 in.

Answer 1

The lengths that make the sense for the value of b are 0.5 inches and 2 inches.

Given

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.

What is the triangle inequality theorem?

If two sides of a triangle are unequal, the longer side has a greater angle opposite to it.

$\rm a+a > b\\\\2a > b$

The equation of the perimeter of the triangle;

$\rm 2a+b = 15.7\\\\2a = 15.7-b\\\\a = \dfrac{15.7-b}{2}$

1. Substitute b = 0.5 in the equation;

$\rm a = \dfrac{15.7-b}{2}\\\\ a = \dfrac{15.7-0.5}{2} \\\\ a = \dfrac{15.2}{2}\\\\a = 7.6$

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;

$\rm a = \dfrac{15.7-b}{2}\\\\ a = \dfrac{15.7-02}{2} \\\\ a = \dfrac{13.7}{2}\\\\a = 6.85$

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.

https://brainly.com/question/1026055