This handy Math in Focus Grade 5 Workbook Answer Key Chapter 13 Practice 4 Triangle Inequalities provides detailed solutions for the textbook questions.

## Math in Focus Grade 5 Chapter 13 Practice 4 Answer Key Triangle Inequalities

**Complete. Measure the sides of the triangle to the nearest half-inch. Then fill in the blanks.**

Explanation:

Question 1.

AB = _________ in.

Answer:

AB = 12 in.

Explanation:

With the help of ruler measured the length and updated

Question 2.

BC = _________ in.

Answer:

BC = 12 in.

Explanation:

With the help of ruler measured the length and updated

Question 3.

AC = ________ in.

Answer:

AC = 7 in.

Explanation:

With the help of ruler measured the length and updated

Question 4.

AB + BC = ________ in.

Answer:

AB + BC = 12 + 12 = 24 in.

Explanation:

With the help of ruler measured the length and updated

AB + BC = 12 + 12 = 24 in.

Question 5.

BC + AC = ________ in.

Answer: 12 + 7 = 19 in.

Explanation:

BC + AC =12 + 7 = 19 in.

With the help of ruler measured the length and updated

Question 6.

AB + AC = ________ in.

Answer:12 + 7 = 19 in.

Explanation:

AB + AC = 12 + 7 = 19 in.

With the help of ruler measured the length and updated

**Use your answers ¡n Exercises 4 to 6. Fill ¡n the blanks with Yes or No.**

Question 7.

Is AB + BC > AC? ______

Answer: Yes

Explanation:

AB + BC = 12 + 12 = 24

AC= 7

24 > 7

Question 8.

Is BC + AC > AB? ______

Answer: Yes

Explanation:

BC + AC = 12 + 7 = 19 in.

AB = 12 in.

19 > 7

Question 9.

Is AB + AC > BC? _______

Answer: Yes

Explanation:

AB + AC = 12 + 7 = 19 in.

BC = 12 in.

19 > 12

**Complete. Measure the sides of the triangle to the nearest centimeter. Then fill in the blanks.**

Explanation:

Question 10.

XY = ___ cm

Answer:

XY = 6 cm

Explanation:

With the help of ruler measured the length and updated

Question 11.

YZ = __ cm

Answer:

YZ = 4 cm

Explanation:

With the help of ruler measured the length and updated

Question 12.

XZ = __ cm

Answer:

XZ = 7 cm

Explanation:

With the help of ruler measured the length and updated

Question 13.

XY + YZ = __ cm

Answer:

XY + YZ = 6 + 4 = 10 cm

Explanation:

XY + YZ =6 + 4 = 10 cm

With the help of ruler measured the length and updated

Question 14.

YZ + XZ = __ cm

Answer:

YZ + XZ = 4 + 7 = 11 cm

Explanation:

YZ + XZ = 4 + 7 = 11 cm

With the help of ruler measured the length and updated

Question 15.

XY + XZ = __ cm

Answer:

XY + XZ = 6 + 7 = 13 cm

Explanation:

XY + XZ = 6 + 7 = 13 cm

With the help of ruler measured the length and updated

**Use your answers in Exercises 10 to 15. Write the sides of the triangle to make the inequalities true.**

Question 16.

XY + YZ > ______

Answer:

XY + YZ > XZ

Explanation:

XY + YZ > XZ

XY + YZ = 6 + 4 = 10 cm

XZ = 7

10 > 7

Question 17.

YZ + XZ > ______

Answer:

YZ + XZ > XY

Explanation:

YZ + XZ > XY

YZ + XZ = 4 + 7 = 11 cm

XY = 6

11 > 6

Question 18.

XY + XZ > ___

Answer:

XY + XZ > YZ

Explanation:

XY + XZ > YZ

XY + XZ = 6 + 7 = 13 cm

YZ = 4

13 > 4

**Show whether it is possible to form triangles with these lengths.**

Question 19.

6 in., 8 in., 12 in.

Answer:

Yes

Explanation:

6+ 8 > 12

6 + 12 > 8

12 + 8 > 6

sum of two sides should be greater than other side. so its possible to form triangle.

Question 20.

9 in., 13 in., 3 in.

Answer:

No

Explanation:

9 + 13 > 3

13 + 3 > 9

9 + 3 < 13 – sum of two sides should be greater than other side. so not possible to form triangle.

Question 21.

2 cm, 4 cm, 7 cm

Answer:

No

Explanation:

2 + 4 < 7

– sum of two sides should be greater than other side. so not possible to form triangle.

**The lengths of two sides of each triangle are given. Name a possible length for the third side. The lengths are in whole centimeters or whole inches.**

Question 22.

AB is greater than 10 centimeters. A possible length for \(\overline{A B}\) is

____ centimeters.

Answer:

15 centimeters

Explanation:

the sum of any 2 sides of a triangle must be greater than the measure of the third side.

13 + 9 > 15

13 + 15 > 9

15 + 9 > 13

Question 23.

QR is greater than 9 inches. A possible length for \(\overline{Q R}\) is

____________ inches.

Answer:

11 inches

Explanation:

the sum of any 2 sides of a triangle must be greater than the measure of the third side.

17 + 8 > 11

17 + 11 > 8

8 + 11 > 17

Solve.

Question 24.

In the triangle EFG, EF = 21 centimeters, FG = 11 centimeters. The length of \(\overline{E G}\) is in whole centimeters and is greater than 25 centimeters. What is a possible length of \(\overline{E G}\) ?

Answer: \(\overline{E G}\) = 26 centimeters

Explanation:

the sum of any 2 sides of a triangle must be greater than the measure of the third side.

21 + 11 > 26

21 + 26 > 11

26 + 11 > 21