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

c

d

Explanation:

just took the test

Answer 2

0.5 in and 2 in

Explanation:

we have

2a+b=15.7

Verify each case

case A) -2 in

this length does not make sense for a possible value of b

case B) 0 in

this length does not make sense for a possible value of b

case C) 0.5 in

Find the value of a

2a+b=15.7

2a+0.5=15.7

2a=15.2

a=7.6 in

Verify the triangle inequality theorem

0.5+7.6 > 7.6 -----> is true

7.6+7.6 > 0.5 -----> is true

therefore

this length does make sense for a possible value of b

case D) 2 in

Find the value of a

2a+b=15.7

2a+2=15.7

2a=13.7

a=6.85 in

Verify the triangle inequality theorem

2+6.85 > 6.85 -----> is true

6.85+6.85 > 2 -----> is true

therefore

this length does make sense for a possible value of b

case E) 7.9 in

Find the value of a

2a+b=15.7

2a+7.9=15.7

2a=7.8

a=3.9 in

Verify the triangle inequality theorem

7.9+3.9 > 3.9 -----> is true

3.9+3.9 > 7.9 -----> is not true

therefore

this length does not make sense for a possible value of b