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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

1 Answer

5 votes

Answer:


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

User Rashed Hasan
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