Question

do these problems and get 100 points 1. 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. c 22 and 15 2 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. d 13.2 and 6.7 3 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. e 34 and 12 4 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. f 23 and 44

Answer 1

`7 < x < 37` -- Triangle 1

`6.5 < x < 19.9` -- Triangle 2

`22 < x < 46` -- Triangle 3

`21 < x < 67` -- Triangle 4

Explanation:

Given

2 sides of a triangle

1. 22 and 15

2. 13.2 and 6.7

3. 34 and 12

4. 23 and 44

Required

Determine the range of the third side in the above triangles

Triangle 1: 22 and 15

Represent the third side with x

We'll make use of the following conditions to calculate the range of the third side;

`22 + x > 15`

`22 + 15 > x`

`15 + x > 22`

Solving

`22 + x > 15`

Make x the subject of formula

`x > 15 - 22`

`x > -7`

Solving

`22 + 15 > x`

`37 > x`

Solving

`15 + x > 22`

Make x the subject of formula

`x > 22 - 15`

`x > 7`

The next step is to dismiss the inequality with negative digit; So, we're left with

`37 > x` and
`x > 7`

Rewrite both inequalities

`x < 37` and
`7 < x`

Combine the two inequalities

`7 < x < 37`

Triangle 2: 13.2 and 6.7

Represent the third side with x

We'll make use of the following conditions to calculate the range of the third side;

`13.2 + x > 6.7`

`13.2 + 6.7 > x`

`6.7 + x > 13.2`

Solving

`13.2 + x > 6.7`

Make x the subject of formula

`x > 6.7 - 13.2`

`x > -6.5`

Solving

`13.2 + 6.7 > x`

`19.9 > x`

Solving

`6.7 + x > 13.2`

Make x the subject of formula

`x > 13.2 - 6.7`

`x > 6.5`

The next step is to dismiss the inequality with negative digit; So, we're left with

`19.9 > x` and
`x > 6.5`

Rewrite both inequalities

`x < 19.9` and
`6.5 < x`

Combine the two inequalities

`6.5 < x < 19.9`

Triangle 3: 34 and 12

Represent the third side with x

We'll make use of the following conditions to calculate the range of the third side;

`34 + x > 12`

`34 + 12 > x`

`12 + x > 34`

Solving

`34 + x > 12`

Make x the subject of formula

`x > 12 - 34`

`x > -22`

Solving

`34 + 12 > x`

`46 > x`

Solving

`12 + x > 34`

Make x the subject of formula

`x > 34 - 12`

`x > 22`

The next step is to dismiss the inequality with negative digit; So, we're left with

`46 > x` and
`x > 22`

Rewrite both inequalities

`x < 46` and
`22 < x`

Combine the two inequalities

`22 < x < 46`

Triangle 4: 23 and 44

Represent the third side with x

We'll make use of the following conditions to calculate the range of the third side;

`23 + x > 44`

`23 + 44 > x`

`23 + x > 44`

Solving

`23 + x > 44`

Make x the subject of formula

`x > 23 - 44`

`x > -21`

Solving

`23 + 44 > x`

`67 > x`

Solving

`23 + x > 44`

Make x the subject of formula

`x > 44 - 23`

`x > 21`

The next step is to dismiss the inequality with negative digit; So, we're left with

`67 > x` and
`x > 21`

Rewrite both inequalities

`x < 67` and
`21 < x`

Combine the two inequalities

`21 < x < 67`