SOLUTION: 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. Which lengths make

Algebra ->  Triangles -> SOLUTION: 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. Which lengths make      Log On


   

Question 1129877: 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.
Which lengths make sense for possible values of b? Check all that apply.
–2 in.
0 in.
0.5 in.
2 in.
7.9 in.
Answer by math_helper(2461) About Me  (Show Source):
You can put this solution on YOUR website!
0.5in and 2in are both possible.

For a proper triangle with sides x,y,z, the triangle inequalities must hold: z < x+y, x < y+z, y < x+z

0in is the degenerate case where one side has zero length (so it collapses to a line, and is not a proper triangle). Also +0+%2B+15.7%2F2+ ≯ +15.7%2F2+

7.9in is too long for b, as the other sides will be (15.7-7.9)/2 = 3.9in and it won't form a closed figure. Notice +3.9+%2B+3.9+ ≯ +7.9+

-2in is nonsensical, a >0, b>0 must be true.