Grade 8 · Math · Unit 6 of 8
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.
NWT Curriculum learning standard: Pythagorean theorem: finding side lengths and testing for right triangles
How we explain it
Children can open this short lesson before they practise.
- It works for right triangles only.
- The two shorter sides (legs) are a and b. The longest side, across from the right angle, is c.
- 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.
Question 1
A right triangle has legs of 84 cm and 80 cm. How long is the hypotenuse?
answer boxcm
116 cm
Hint: c² = a² + b² = 7056 + 6400 = 13456, so c = √13456 = 116 cm.
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
20 cm
Hint: b² = c² − a² = 841 − 441 = 400, so b = √400 = 20 cm.
Question 3
A triangle has sides 80 cm, 84 cm and 116 cm. Is it a right triangle?
- Yes
- No
Yes
Hint: Check whether 80² + 84² = 116²: 6400 + 7056 = 13456, and 116² = 13456. They match.
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
51 m
Hint: The wall, ground and ladder make a right triangle. c² = 24² + 45² = 2601, so c = 51 m.
Question 5
A rectangular field is 72 m by 21 m. How long is the diagonal across the field?
answer boxm
75 m
Hint: The diagonal is the hypotenuse of a right triangle with legs 72 m and 21 m: √(5184 + 441) = √5625 = 75 m.
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
6.7 cm
Hint: c² = 3² + 6² = 45. √45 ≈ 6.7.