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Pythagoras Theorem - Year 6 Quick Test

Math Worksheet

  1. A right-angled triangle has legs of length $3$ cm and $4$ cm. What is the length of its hypotenuse?

  2. Find the hypotenuse of a right triangle with legs $5$ cm and $12$ cm.

  3. In a right triangle, the hypotenuse is $13$ cm and one leg is $5$ cm. Find the length of the other leg.

  4. A ladder is leaning against a wall. The foot of the ladder is $6$ m from the wall, and the ladder’s length is $10$ m. How high up the wall does the ladder reach?

  5. A right triangle has one leg $7$ cm and hypotenuse $25$ cm. Find the length of the other leg.

  6. The diagonal of a rectangle measures $13$ cm, and one side is $5$ cm. Find the length of the other side of the rectangle.

  7. A right triangle has legs of length $8$ m and $15$ m. Find the length of its hypotenuse.

  8. Find the diagonal of a square whose side is $9$ cm.

  9. A television screen is $40$ cm wide and $30$ cm tall. What is the length of its diagonal?

  10. One leg of a right triangle is $9$ cm, and the hypotenuse is $15$ cm. Find the length of the other leg.

  11. A right triangle’s legs are $12$ m and $16$ m. Find the length of its hypotenuse.

  12. A right triangle has legs of length $6$ cm and $12$ cm. Find the length of its hypotenuse, rounded to three decimal places.

  13. A rectangle measures $5$ m by $12$ m. What is the length of its diagonal?

  14. A right triangle has hypotenuse $17$ cm and one leg $8$ cm. Find the length of the other leg.

  15. Find the length of the hypotenuse of a right triangle when both legs are $7$ cm.

  16. A ramp makes a right triangle with a horizontal run of $4$ m and a vertical rise of $3$ m. How long is the ramp?

  17. In a right triangle, the hypotenuse is $26$ cm and one leg is $10$ cm. Find the length of the other leg.

  18. A rectangle measures $20$ cm by $21$ cm. Find the length of its diagonal.

  19. A right triangle has legs $14$ cm and $48$ cm. Find the length of its hypotenuse.

  20. Question 20 Image

    Find the distance between points $(-3, 1)$ and $(5, -3)$ in the coordinate plane, rounded to three decimal places.

Answer Sheet

  1. A right-angled triangle has legs of length $3$ cm and $4$ cm. What is the length of its hypotenuse? → 5 cm
  2. Find the hypotenuse of a right triangle with legs $5$ cm and $12$ cm. → 13 cm
  3. In a right triangle, the hypotenuse is $13$ cm and one leg is $5$ cm. Find the length of the other leg. → 12 cm
  4. A ladder is leaning against a wall. The foot of the ladder is $6$ m from the wall, and the ladder’s length is $10$ m. How high up the wall does the ladder reach? → 8 m
  5. A right triangle has one leg $7$ cm and hypotenuse $25$ cm. Find the length of the other leg. → 24 cm
  6. The diagonal of a rectangle measures $13$ cm, and one side is $5$ cm. Find the length of the other side of the rectangle. → 12 cm
  7. A right triangle has legs of length $8$ m and $15$ m. Find the length of its hypotenuse. → 17 m
  8. Find the diagonal of a square whose side is $9$ cm. → $9\sqrt{2}$ cm
  9. A television screen is $40$ cm wide and $30$ cm tall. What is the length of its diagonal? → 50 cm
  10. One leg of a right triangle is $9$ cm, and the hypotenuse is $15$ cm. Find the length of the other leg. → 12 cm
  11. A right triangle’s legs are $12$ m and $16$ m. Find the length of its hypotenuse. → 20 m
  12. A right triangle has legs of length $6$ cm and $12$ cm. Find the length of its hypotenuse, rounded to three decimal places. → $6\sqrt{5} \approx 13.416$ cm
  13. A rectangle measures $5$ m by $12$ m. What is the length of its diagonal? → 13 m
  14. A right triangle has hypotenuse $17$ cm and one leg $8$ cm. Find the length of the other leg. → 15 cm
  15. Find the length of the hypotenuse of a right triangle when both legs are $7$ cm. → $7\sqrt{2}$ cm
  16. A ramp makes a right triangle with a horizontal run of $4$ m and a vertical rise of $3$ m. How long is the ramp? → 5 m
  17. In a right triangle, the hypotenuse is $26$ cm and one leg is $10$ cm. Find the length of the other leg. → 24 cm
  18. A rectangle measures $20$ cm by $21$ cm. Find the length of its diagonal. → 29 cm
  19. A right triangle has legs $14$ cm and $48$ cm. Find the length of its hypotenuse. → 50 cm
  20. Question 20 ImageFind the distance between points $(-3, 1)$ and $(5, -3)$ in the coordinate plane, rounded to three decimal places. → $4\sqrt{5} \approx 8.944$