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Grade 8 · Math · Unit 8 of 11

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.

Saskatchewan Curriculum outcome: SS8.1 · 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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