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Lesson 3: Apply the Pythagorean Theorem to Solve Problems — Practice Questions

  1. 1. A rectangular garden is 7 meters wide and 24 meters long. A diagonal path connects opposite corners. What is the length of this path in meters? The length is ___ meters.

  2. 2. A 26-foot support wire is attached to the top of a flagpole. The wire is anchored to the ground 10 feet from the base of the pole. How tall is the flagpole?

    • A. 24 feet
    • B. 28 feet
    • C. 16 feet
    • D. $\sqrt{776}$ feet
  3. 3. A drone flies 15 km south from its base, then turns and flies 20 km west. What is the straight-line distance from the drone back to its base? The distance is ___ km.

  4. 4. In a right triangle, the hypotenuse is 13 cm long and one of the legs is 5 cm long. What is the length of the other leg? The length is ___ cm.

  5. 5. A wheelchair ramp is 10 meters long and reaches a loading dock that is 6 meters high. What is the horizontal distance covered by the ramp from the base of the dock?

    • A. 8 meters
    • B. 4 meters
    • C. 16 meters
    • D. $\sqrt{136}$ meters
  6. 6. A rectangular garden is 8 meters wide and 15 meters long. A straight path connects two opposite corners. What is the length of the path in meters? ___

  7. 7. A 25-foot support wire is attached to the top of a vertical pole. The wire is anchored to the ground 7 feet from the pole's base. How tall is the pole in feet? ___

  8. 8. A wheelchair ramp covers a horizontal distance of 12 feet to reach a doorway 5 feet high. What is the length of the ramp's surface in feet? ___

  9. 9. A 9-meter tall flagpole casts a shadow that is 12 meters long. What is the distance from the top of the flagpole to the tip of its shadow?

    • A. 15 meters
    • B. 21 meters
    • C. 3 meters
    • D. 7.9 meters
  10. 10. A playground slide is 10 feet long. Its base on the ground is 6 feet away from the ladder. How high is the top of the slide from the ground, in feet? ___