Question

Please help, due in an hour. Two sides of a triangle are 12cm and 8cm. Complete the inequality to show the possible lengths for the third side. If the third side of the triangle is x then, _

Answer 1

`4 < x < 20`

Explanation:

By the triangle inequality theorem, the sum of the length of the two smaller sides must be greater than the length of the largest side. If 12 cm was the length of the largest side, notice that
`8+x > 12 \Rightarrow x > 4`. Similarly, if x was the length of the largest side, we'd get the inequality
`12+8 > x \Rightarrow 20 > x`. Combining these inequalities, we get
`\boxed{4 < x < 20}`.