directions: could the set of numbers be the three sides of a right triangle? write yes or no.
7. 6, 12, and 13
8. 14, 48, and 50
9. 10, 18, and 22

7. 8, 15, and 17
8. 20, 21, and 30
9. 20, 21, and 29

directions: find the missing measurement. round to the nearest tenth if necessary.
10. a =
b = 60
c = 61
11. a = 30
b = 16
c =
12. a = 5
b =
c = 11

Question

directions: could the set of numbers be the three sides of a right triangle? write yes or no.
7. 6, 12, and 13
8. 14, 48, and 50
9. 10, 18, and 22

7. 8, 15, and 17
8. 20, 21, and 30
9. 20, 21, and 29

directions: find the missing measurement. round to the nearest tenth if necessary.
10. a =
    b = 60
    c = 61
11. a = 30
    b = 16
    c =
12. a = 5
    b =
    c = 11

Accepted Answer

### Problem 7 (6, 12, 13)
# Explanation:
## Step1: Identify hypotenuse (longest side)
Longest side is 13. So $ c = 13 $, $ a = 6 $, $ b = 12 $.
## Step2: Apply Pythagorean theorem ($ a^2 + b^2 = c^2 $)
Calculate $ 6^2 + 12^2 = 36 + 144 = 180 $, $ 13^2 = 169 $. Since $ 180
eq 169 $, not a right triangle.
# Answer: No

### Problem 8 (14, 48, 50)
# Explanation:
## Step1: Identify hypotenuse (50)
$ a = 14 $, $ b = 48 $, $ c = 50 $.
## Step2: Apply Pythagorean theorem
$ 14^2 + 48^2 = 196 + 2304 = 2500 $, $ 50^2 = 2500 $. Since $ 2500 = 2500 $, it is a right triangle.
# Answer: Yes

### Problem 9 (10, 18, 22)
# Explanation:
## Step1: Identify hypotenuse (22)
$ a = 10 $, $ b = 18 $, $ c = 22 $.
## Step2: Apply Pythagorean theorem
$ 10^2 + 18^2 = 100 + 324 = 424 $, $ 22^2 = 484 $. Since $ 424
eq 484 $, not a right triangle.
# Answer: No

### Problem 7 (8, 15, 17)
# Explanation:
## Step1: Identify hypotenuse (17)
$ a = 8 $, $ b = 15 $, $ c = 17 $.
## Step2: Apply Pythagorean theorem
$ 8^2 + 15^2 = 64 + 225 = 289 $, $ 17^2 = 289 $. Since $ 289 = 289 $, it is a right triangle.
# Answer: Yes

### Problem 8 (20, 21, 30)
# Explanation:
## Step1: Identify hypotenuse (30)
$ a = 20 $, $ b = 21 $, $ c = 30 $.
## Step2: Apply Pythagorean theorem
$ 20^2 + 21^2 = 400 + 441 = 841 $, $ 30^2 = 900 $. Since $ 841
eq 900 $, not a right triangle.
# Answer: No

### Problem 9 (20, 21, 29)
# Explanation:
## Step1: Identify hypotenuse (29)
$ a = 20 $, $ b = 21 $, $ c = 29 $.
## Step2: Apply Pythagorean theorem
$ 20^2 + 21^2 = 400 + 441 = 841 $, $ 29^2 = 841 $. Since $ 841 = 841 $, it is a right triangle.
# Answer: Yes

### Problem 10 (a =?, b = 60, c = 61)
# Explanation:
## Step1: Apply Pythagorean theorem ($ a^2 + b^2 = c^2 $)
Rearrange to $ a^2 = c^2 - b^2 $.
## Step2: Substitute values
$ a^2 = 61^2 - 60^2 = 3721 - 3600 = 121 $.
## Step3: Solve for a
$ a = \sqrt{121} = 11 $.
# Answer: 11

### Problem 11 (a = 30, b = 16, c =?)
# Explanation:
## Step1: Apply Pythagorean theorem ($ a^2 + b^2 = c^2 $)
## Step2: Substitute values
$ c^2 = 30^2 + 16^2 = 900 + 256 = 1156 $.
## Step3: Solve for c
$ c = \sqrt{1156} = 34 $.
# Answer: 34

### Problem 12 (a = 5, b =?, c = 11)
# Explanation:
## Step1: Apply Pythagorean theorem ($ a^2 + b^2 = c^2 $)
Rearrange to $ b^2 = c^2 - a^2 $.
## Step2: Substitute values
$ b^2 = 11^2 - 5^2 = 121 - 25 = 96 $.
## Step3: Solve for b
$ b = \sqrt{96} \approx 9.8 $ (rounded to nearest tenth).
# Answer: 9.8

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QUESTION IMAGE

Question

Explanation:

Problem 7 (6, 12, 13)

Step1: Identify hypotenuse (longest side)

Step2: Apply Pythagorean theorem (\( a^2 + b^2 = c^2 \))

Step1: Identify hypotenuse (50)

Step2: Apply Pythagorean theorem

Step1: Identify hypotenuse (22)

Step2: Apply Pythagorean theorem

Answer:

Problem 8 (14, 48, 50)