Grade 9 · Math · Unit 13 of 15
Right Triangles & Scaling
Pythagoras and changing dimensions
What your child practises
Using the Pythagorean relationship for ladders, ramps, roofs and diagonals, deciding whether a triangle is right-angled, and seeing how doubling or tripling dimensions changes perimeter, area and volume.
Ontario Curriculum expectation: E1.2, E1.4, E1.5 · triangle and circle properties, the right-triangle relationship, and how scaling affects measures
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 triangle has sides 9 cm, 40 cm and 41 cm. Is it a right triangle?
- No, it is not a right triangle
- Yes, it is a right triangle
Show answer
Yes, it is a right triangle
Hint: Check whether 9² + 40² equals 41²: 81 + 1600 = 1681 and 41² = 1681.
Question 2
An isosceles triangle has an apex angle of 50°. How big is each of the two equal base angles?
answer box°
Show answer
65 °
Hint: The angles add to 180°. (180 − 50) ÷ 2 = 65.
Question 3
A 29 m ladder leans on a wall with its foot 20 m from the wall. How high up the wall does it reach, in metres?
answer boxm
Show answer
21 m
Hint: Use a² + b² = c²: 400 + b² = 841, so b² = 441 and b = 21.
Question 4
The end of a roof is an isosceles triangle with a base of 18 m and two equal sloping sides of 15 m. How tall is it, in metres?
answer boxm
Show answer
12 m
Hint: Split the triangle in half: a right triangle with hypotenuse 15 and base 9. The height is √(225 − 81) = 12.
Question 5
A ramp has a horizontal run of 7 m and a rise of 24 m. How long is the sloping surface, in metres?
answer boxm
Show answer
25 m
Hint: Use a² + b² = c²: 49 + 576 = 625, so c = 25.
Question 6
A rectangle is 6 cm by 8 cm. Its width is multiplied by 2, and its height stays the same. What is the new area, in cm²?
answer boxcm²
Show answer
96 cm²
Hint: New width = 12 cm. Area = 12 × 8 = 96.