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. 0.5 , D. 2

Explanation:

Answer 2

`0.5\ in`

`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