L27 · Apply the Pythagorean theorem

1. 1.

   A rectangle is 3 by 4. How long is a diagonal?

   Answer. 5

   Diagonal² = 3² + 4² = 5², so the diagonal is 5.

2. 2.

   Find the missing leg of a right triangle with leg 5 and hypotenuse 13.

   Answer. 12

   x² + 5² = 13² → x² = 144 → x = 12.

3. 3.

   A rectangle is 8 by 15. How long is a diagonal?

   Answer. 17

   Diagonal² = 8² + 15² = 17², so the diagonal is 17.

4. 4.

   A rectangle is 6 by 8. How long is a diagonal?

   Answer. 10

   Diagonal² = 6² + 8² = 10², so the diagonal is 10.

5. 5.

   A rectangle is 6 by 8. How long is a diagonal? Then Owen needs 4 of that amount. What is the total they need?

   Answer. 40

   Diagonal² = 6² + 8² = 10², so the diagonal is 10. Then multiply by 4: 40.

6. 6.

   Find the missing leg of a right triangle with leg 3 and hypotenuse 5. Then Ava needs 5 of that amount. What is the total they need?

   Answer. 20

   x² + 3² = 5² → x² = 16 → x = 4. Then multiply by 5: 20.

7. 7.

   A rectangle is 8 by 15. How long is a diagonal? Then Mei needs 4 of that amount. What is the total they need?

   Answer. 68

   Diagonal² = 8² + 15² = 17², so the diagonal is 17. Then multiply by 4: 68.

8. 8.

   Find the missing leg of a right triangle with leg 12 and hypotenuse 37. Then Sam needs 3 of that amount. What is the total they need?

   Answer. 105

   x² + 12² = 37² → x² = 1225 → x = 35. Then multiply by 3: 105.

9. 9.

   A rectangle is 12 by 16. How long is a diagonal? Then Priya needs 2 of that amount. What is the total they need?

   Answer. 40

   Diagonal² = 12² + 16² = 20², so the diagonal is 20. Then multiply by 2: 40.

10. 10.

    A rectangle is 5 by 12. How long is a diagonal? Then Ava needs 4 of that amount. What is the total they need?

    Answer. 52

    Diagonal² = 5² + 12² = 13², so the diagonal is 13. Then multiply by 4: 52.

11. 11.

    Think

    Luis tried this problem:
    Find the missing leg of a right triangle with leg 12 and hypotenuse 20.
    Luis wrote 32. That is not correct. What is the right answer?

    Answer. 16

    Luis’s answer 32 is off. x² + 12² = 20² → x² = 256 → x = 16.

12. 12.

    Think

    Theo tried this problem:
    Find the missing leg of a right triangle with leg 9 and hypotenuse 41.
    Theo wrote -40. That is not correct. What is the right answer?

    Answer. 40

    Theo’s answer -40 is off. x² + 9² = 41² → x² = 1600 → x = 40.

Original extra practice. Keys are computed from the items, not guessed.