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Grade 8 · Math · Unit 8 of 13

Pythagorean Theorem

Right triangles and a² + b² = c²

What your child practises

Finding a missing side of a right triangle, checking whether a triangle is a right triangle, and using the theorem for ladders and diagonals.

Alberta Curriculum learning outcome: SS1 · developing and applying the Pythagorean theorem

How we explain it

Children can open this short lesson before they practise.

  1. It works for right triangles only.
  2. The two shorter sides (legs) are a and b. The longest side, across from the right angle, is c.
  3. a² + b² = c².

Example: A right triangle has legs 6 cm and 8 cm. How long is the longest side? 6² + 8² = 36 + 64 = 100. c = √100 = 10. Answer: 10 cm

Sample questions

A taste of this unit. In the app, questions change every time and get easier or harder to match your child.

  1. Question 1

    A right triangle has legs of 84 cm and 80 cm. How long is the hypotenuse?

    answer boxcm

    Show answer

    116 cm

    Hint: c² = a² + b² = 7056 + 6400 = 13456, so c = √13456 = 116 cm.

  2. Question 2

    The hypotenuse of a right triangle is 29 cm and one leg is 21 cm. How long is the other leg?

    answer boxcm

    Show answer

    20 cm

    Hint: b² = c² − a² = 841 − 441 = 400, so b = √400 = 20 cm.

  3. Question 3

    A triangle has sides 80 cm, 84 cm and 116 cm. Is it a right triangle?

    • Yes
    • No
    Show answer

    Yes

    Hint: Check whether 80² + 84² = 116²: 6400 + 7056 = 13456, and 116² = 13456. They match.

  4. Question 4

    A ladder leans against a wall. Its foot is 24 m from the wall and it reaches 45 m up the wall. How long is the ladder?

    answer boxm

    Show answer

    51 m

    Hint: The wall, ground and ladder make a right triangle. c² = 24² + 45² = 2601, so c = 51 m.

  5. Question 5

    A rectangular field is 72 m by 21 m. How long is the diagonal across the field?

    answer boxm

    Show answer

    75 m

    Hint: The diagonal is the hypotenuse of a right triangle with legs 72 m and 21 m: √(5184 + 441) = √5625 = 75 m.

  6. Question 6

    The legs of a right triangle are 3 cm and 6 cm. What is the hypotenuse, rounded to 1 decimal place?

    • 5.2 cm
    • 9.0 cm
    • 6.7 cm
    • 6.8 cm
    Show answer

    6.7 cm

    Hint: c² = 3² + 6² = 45. √45 ≈ 6.7.

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