Pythagorean Theorem: Score: Name | Download Free PDF | Length ... - Free Printable

I'll solve each problem step by step using the Pythagorean Theorem (a² + b² = c²).

Problem 1:
Mark drives 35 miles North and 42 miles West. We need to find the shortest distance (diagonal) home.

Using Pythagorean Theorem:
- a = 35, b = 42
- c² = 35² + 42²
- c² = 1,225 + 1,764
- c² = 2,989
- c = √2,989 ≈ 54.7 miles

Problem 2:
Laptop screen is 10 inches high and 24 inches wide. Find the diagonal.

Using Pythagorean Theorem:
- a = 10, b = 24
- c² = 10² + 24²
- c² = 100 + 576
- c² = 676
- c = √676 = 26 inches

Problem 3:
Sandwich is 4 inches long and 6 inches high. Find the diagonal when cut in half.

Using Pythagorean Theorem:
- a = 4, b = 6
- c² = 4² + 6²
- c² = 16 + 36
- c² = 52
- c = √52 ≈ 7.2 inches

Problem 4:
Tree is 15 feet tall, shadow is 8 feet long. Find distance from tip of tree to tip of shadow.

Using Pythagorean Theorem:
- a = 15, b = 8
- c² = 15² + 8²
- c² = 225 + 64
- c² = 289
- c = √289 = 17 feet

Problem 5:
Rug is 11 feet long and 9 feet wide. Find the diagonal.

Using Pythagorean Theorem:
- a = 11, b = 9
- c² = 11² + 9²
- c² = 121 + 81
- c² = 202
- c = √202 ≈ 14.2 feet

Final Answer:
1) 54.7 miles
2) 26 inches
3) 7.2 inches
4) 17 feet
5) 14.2 feet