Question

NO LINKS!! URGENT HELP PLEASE!!!! Part 1

For 7 & 9, Given two sides of a triangle, find a range of possible lengths for the 3rd side.

For #11, If a triangle has lengths of 27 m and 11 m, check all the possible lengths for the 3rd side.

Answer 1

• 7) The third side is between 13 cm and 21 cm;
• 9) The third side is between 23 cm and 41 cm;
• 11) The possible lengths for the third side are 17 m, 22 m, 35 m.

-----------------------------------

Use triangle inequality theorem:

• The sum of lengths of any two sides is greater than the length of the third side.

Question 7

Given sides:

• 4 cm, 17 cm, x cm

Let the smallest side be 4 cm, then:

• 4 + x > 17 ⇒ x > 13

Let the largest side be x, then:

• x < 4 + 17 = 21

The third side is between 13 cm and 21 cm.

Question 9

Given sides:

• 9 yd, 32 yd, x yd

Let the smallest side be 9 yd, then:

• 9 + x > 32 ⇒ x > 23

Let the largest side be x, then:

• x < 9 + 32 = 41

The third side is between 23 cm and 41 cm

Question 11

Given sides:

• 11 m, 27 m, x m

Let the smallest side be 11 m, then:

• 11 + x > 27 ⇒ x > 16

Let the largest side be x, then:

• x < 11 + 27 = 38

The third side is between 16 m and 38 m.

Correct choices for possible third side lengths are:

• 17 m, 22 m, 35 m

(note it is m not feet or the initial lengths to be in feet)

Answer 2

7. (13, 21)

9. (23, 41)

11. 17 m, 35 m, 22 m

Explanation:

Triangle Inequality Theorem

The sum of any two sides of a triangle is greater than the length of the third side.

Question 7

Let x be the length of the unknown side of the triangle.

Given two sides of a triangle are 4 cm and 17 cm, then:

(a) The sum of the two given sides is greater than the third side:

`\implies 4+17 > x`

`\implies 21 > x`

(a) The longest side is 17 cm:

`\implies 4 + x > 17`

`\implies x > 13`

Therefore, the range of possible lengths for the third side is:

• 13 < x < 21
• Interval notation: (13, 21)

Question 9

Let x be the length of the unknown side of the triangle.

Given two sides of a triangle are 9 yd and 32 yd, then:

(a) The sum of the two given sides is greater than the third side:

`\implies 9+32 > x`

`\implies 41 > x`

(a) The longest side is 32 yd:

`\implies 9 + x > 32`

`\implies x > 23`

Therefore, the range of possible lengths for the third side is:

• 23 < x < 41
• Interval notation: (23, 41)

Question 11

Let x be the length of the unknown side of the triangle.

Given two sides of a triangle are 27 m and 11 m, then:

(a) The sum of the two given sides is greater than the third side:

`\implies 11+27 > x`

`\implies 38 > x`

(a) The longest side is 27 m:

`\implies 11 + x > 27`

`\implies x > 16`

Therefore, the range of possible lengths for the third side is:

• 16 < x < 38
• Interval notation: (16, 38)

Note: There must be an error in the question, since the answer options are in feet rather than in meters. As there is approximately 3.3 ft to 1 meter, if we convert the range to feet, the given answer options are out of range by some margin.

Therefore, assuming the unit of measure of the answer options is supposed to be in meters, the possible lengths for the third side of the triangle are:

• 17 m
• 35 m
• 22 m