Question

Two sides of a triangle have lengths 11 and 18. Write an inequality to represent the possible lengths for the third side, x.

Answer 1

Answer:
`7<x\leq29`

Explanation:

• The triangle inequality tells that for any triangle, the sum of the lengths of any two sides must be greater than or equal to the length of the remaining side.

Given: Two sides of a triangle have lengths 11 and 18.

The third side is represented by x.

So by triangle inequality, we have the following inequality:

`x\leq11+18\\\\\Rightarrow\ x\leq29`

Also, the difference between the lengths of any two sides of a triangle is less than the length of the third side.

`\Rightarrow18-11<x\\\Rightarrow 7<x`

Thus, the inequality to describe the possible side length for the third side is

`7<x\leq29`

Answer 2

Side inequality of triangle states that the sum of any two sides of a triangle should be greater than the third side so the sum of two sides

In this case, 11 + 18 = 29 > 3rd side So 29 > 3rd side or we can say 3rd side < 29

Also, the third side cannot be smaller than the difference of the given two sides so the third side has to be greater than 18-11 = 7 so 3rd side > 7 so if length of 3rd side is represented by x, then 7 < x < 29