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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.

Respuesta :

calculista

Answer:

[tex]0.5\ in[/tex]

[tex]2\ in[/tex]

Step-by-step explanation:

we have

[tex]2a+b=15.7[/tex]

Verify each case

case A) [tex]-2\ in[/tex]

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

case B) [tex]0\ in[/tex]

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

case C) [tex]0.5\ in[/tex]

Find the value of a

[tex]2a+b=15.7[/tex]

[tex]2a+0.5=15.7[/tex]

[tex]2a=15.2[/tex]

[tex]a=7.6\ in[/tex]

Verify the triangle inequality theorem

[tex]0.5+7.6 > 7.6[/tex] -----> is true

[tex]7.6+7.6 > 0.5[/tex] -----> is true

therefore

this length does make sense for a possible value of b

case D) [tex]2\ in[/tex]

Find the value of a

[tex]2a+b=15.7[/tex]

[tex]2a+2=15.7[/tex]

[tex]2a=13.7[/tex]

[tex]a=6.85\ in[/tex]

Verify the triangle inequality theorem

[tex]2+6.85 > 6.85[/tex] -----> is true

[tex]6.85+6.85 > 2[/tex] -----> is true

therefore

this length does make sense for a possible value of b

case E) [tex]7.9\ in[/tex]

Find the value of a

[tex]2a+b=15.7[/tex]

[tex]2a+7.9=15.7[/tex]

[tex]2a=7.8[/tex]

[tex]a=3.9\ in[/tex]

Verify the triangle inequality theorem

[tex]7.9+3.9 > 3.9[/tex] -----> is true

[tex]3.9+3.9 > 7.9[/tex] -----> is not true

therefore

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

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