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

Answer:

$7 < x < 37$ -- Triangle 1

$6.5 < x < 19.9$ -- Triangle 2

$22 < x < 46$ -- Triangle 3

$21 < x < 67$ -- Triangle 4

Step-by-Step 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

$21 < x < 67$