Pythagorean Theorem Coloring By Number - Free Printable

Thank you for uploading the Pythagorean Theorem practice worksheet. I’ll solve each of the 12 problems step by step, using the Pythagorean Theorem:

> a² + b² = c²
> where *a* and *b* are the legs of a right triangle, and *c* is the hypotenuse (the side opposite the right angle).

I’ll also match each answer to its corresponding color code as instructed.

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Problem 1

Given: Legs = 6 m, 8 m
Find: Hypotenuse

Solution:
a² + b² = c²
6² + 8² = c²
36 + 64 = c²
100 = c²
c = √100 = 10

✔ Answer: 10 — Orange

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Problem 2

Given: Leg = 8 in, Hypotenuse = 17 in
Find: Missing leg

Solution:
a² + b² = c² → let a = 8, c = 17, find b
8² + b² = 17²
64 + b² = 289
b² = 289 - 64 = 225
b = √225 = 15

✔ Answer: 15 — Purple

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Problem 3

Given: Legs = 6 cm, 8 cm
Find: Hypotenuse

Solution:
6² + 8² = c²
36 + 64 = 100
c = √100 = 10

✔ Answer: 10 — Black

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Problem 4

Given: Ladder = 10 ft (hypotenuse), base = 6 ft (one leg)
Find: Height up wall (other leg)

Solution:
a² + b² = c² → a = 6, c = 10, find b
6² + b² = 10²
36 + b² = 100
b² = 64
b = √64 = 8

✔ Answer: 8 — Light Green

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Problem 5

Given: Points A(2, 2), B(2, 6) — vertical line
Find: Distance (vertical leg)

Solution:
Since x-coordinates are same, distance = |6 - 2| = 4

✔ Answer: 4 — Pink

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Problem 6

Given: Points A(-1, 3), B(3, 6)
Find: Distance between them (hypotenuse of right triangle formed)

Solution:
Δx = 3 - (-1) = 4
Δy = 6 - 3 = 3
Distance = √(4² + 3²) = √(16 + 9) = √25 = 5

✔ Answer: 5 — Dark Blue

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Problem 7

Given: Horizontal leg = 6 ft, vertical leg = 8 ft
Find: Diagonal (hypotenuse)

Solution:
6² + 8² = c²
36 + 64 = 100
c = √100 = 10

✔ Answer: 10 — Light Blue

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Problem 8

Given: Boat travels 8 mi east, 15 mi north → forms right triangle
Find: Straight-line distance from start (hypotenuse)

Solution:
8² + 15² = c²
64 + 225 = 289
c = √289 = 17

✔ Answer: 17 — Red

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Problem 9

Given: Legs = 5 ft, 12 ft
Find: Hypotenuse

Solution:
5² + 12² = c²
25 + 144 = 169
c = √169 = 13

✔ Answer: 13 — Purple

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Problem 10

Given: Legs = 7 ft, 24 ft
Find: Hypotenuse

Solution:
7² + 24² = c²
49 + 576 = 625
c = √625 = 25

✔ Answer: 25 — Light Green

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Problem 11

Given: Legs = 9 cm, 12 cm
Find: Hypotenuse

Solution:
9² + 12² = c²
81 + 144 = 225
c = √225 = 15

✔ Answer: 15 — Dark Blue

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Problem 12

Given: Legs = 15 cm, 20 cm
Find: Hypotenuse

Solution:
15² + 20² = c²
225 + 400 = 625
c = √625 = 25

✔ Answer: 25 — Black

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## ✔ Final Answer Key (Color-Coded):

| Problem | Answer | Color |
|---------|--------|--------------|
| 1 | 10 | Orange |
| 2 | 15 | Purple |
| 3 | 10 | Black |
| 4 | 8 | Light Green |
| 5 | 4 | Pink |
| 6 | 5 | Dark Blue |
| 7 | 10 | Light Blue |
| 8 | 17 | Red |
| 9 | 13 | Purple |
| 10 | 25 | Light Green |
| 11 | 15 | Dark Blue |
| 12 | 25 | Black |

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You can now use this key to color your picture according to the instructions! Let me know if you need help with the coloring or graphing part too. 😊