Question

a triangle has side lengths for 8 in and 7 in select all the possible lengths for the third side 6 inches 15 inches 7 inches 20 inches 9 inches

Answer 1

To answer this question, we need to take into account the triangular inequality, that is, in a triangle, the sum of two sides must be greater than one side of the triangle. That is:

`a+b>c,b+c>a,a+c>b`

We can see that two of the sides are:

a = 8 in, and b = 7 in, then, we have:

a + b = 8 + 7 = 15. Therefore:

`15>6,\text{ and 15>7,15>9}`

Therefore, the possible lengths for the third side are:

• 6 inches

,

• 7 inches

,

• 9 inches