Question

Given the lengths of two sides of a triangle, find the range for the length of the third side. (Range means find between which two numbers the length of the third side must fall.) Write an inequality. 34 and 12

Answer 1

`22 < X < 46`

Explanation:

Given

Two sides of a triangle; 34 and 12

Required

Determine the range of the third side

Represent the third side with X

To determine the range of the third side; two of the following conditions must be satisfied'

`34 + X > 12`

`34 + 12 > X`

`12 + X > 34`

Solving 34 + X > 12

Subtract 34 from both sides

`34 - 34 + X> 12 - 34`

`X > -22`

Solving 34 + 12 > X

`34 + 12 > X`

`46 > X`

Solving 12+ X > 34

Subtract 12 from both sides

`12 - 12 + X > 34 -12`

`X > 22`

Write out the results

`X > -22`

`46 > X`

`X > 22`

The first inequality will be discarded because it accommodates negative digits;

So, we're left with

`46 > X` and
`X > 22`

This can be rewritten as

`X < 46` and
`22 < X`

Combine both inequalities;

`22 < X < 46`

Hence, the range of the third length is
`22 < X < 46`