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Grade 9 · Math · Unit 7 of 9

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.

Prince Edward Island Curriculum curriculum outcome: 9.SS1 · using the Pythagorean theorem to solve problems

How we explain it

Children can open this short lesson before they practise.

  1. In a right triangle, a² + b² = c², where c is the longest side.
  2. Scaling sides by k scales area by k².
  3. Check that your answer fits the picture.

Example: A right triangle has legs of 3 and 4. What is the hypotenuse? 3² + 4² = 9 + 16 = 25. The square root of 25 is 5. Answer: 5

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 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

  2. Question 2

    An isosceles triangle has an apex angle of 50°. How big is each of the two equal base angles?

    answer box°

  3. 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

  4. 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

  5. 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

  6. 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

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