- Problem 1a: The legs are 7 cm and 12 cm. Using the Pythagorean theorem, c² = 7² + 12² = 49 + 144 = 193. So, c = √193 ≈ 13.9 cm. Cross out "ON".
- Problem 1b: The legs are 8 ft and 15 ft. Using the Pythagorean theorem, c² = 8² + 15² = 64 + 225 = 289. So, c = √289 = 17 ft. Cross out "UM".
- Problem 1c: The legs are both 10 in. Using the Pythagorean theorem, c² = 10² + 10² = 100 + 100 = 200. So, c = √200 ≈ 14.1 in. Cross out "E".
- Problem 2: The pole (8 ft) and the ground distance (5 ft) form the legs of a right triangle. The wire is the hypotenuse. c² = 8² + 5² = 64 + 25 = 89. So, c = √89 ≈ 9.4 ft. Cross out "B".
- Problem 3: The vertical rise (300 m) and horizontal flight (400 m) form the legs of a right triangle. The distance from the start is the hypotenuse. c² = 300² + 400² = 90,000 + 160,000 = 250,000. So, c = √250,000 = 500 m. Cross out "IT".
- Problem 4a: On the dot paper, the triangle has legs of 2 cm and 2 cm. The hypotenuse is √(2² + 2²) = √8 ≈ 2.8 cm. The perimeter is 2 + 2 + 2.8 = 6.8 cm. Cross out "AN".
- Problem 4b: On the dot paper, the triangle has legs of 2 cm and 3 cm. The hypotenuse is √(2² + 3²) = √13 ≈ 3.6 cm. The perimeter is 2 + 3 + 3.6 = 8.6 cm. Cross out "ME".
- Problem 5: Walking 70 paces north and 40 paces east forms a right triangle. The straight-line distance is the hypotenuse. c² = 70² + 40² = 4900 + 1600 = 6500. So, c = √6500 ≈ 80.6 paces. Cross out "T".
- Problem 6: The distance from home plate to second base is the diagonal of a square with sides of 60 ft. c² = 60² + 60² = 3600 + 3600 = 7200. So, c = √7200 ≈ 84.9 ft. Cross out "L".
- Problem 7: Walking along two sides is 2 mi + 1.5 mi = 3.5 mi. Walking diagonally is the hypotenuse of a rectangle: c² = 2² + 1.5² = 4 + 2.25 = 6.25. So, c = √6.25 = 2.5 mi. The difference is 3.5 - 2.5 = 1 mi. Cross out "D".
The remaining letters are A, M, A, R, T, I, A, N, B, A, N, D. Reading them in order gives "A MARTIAN BAND".
Parent Tip: Review the logic above to help your child master the concept of marcy mathworks worksheet answers.
