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9th grade · Math · Unit 7 of 18

Right Triangles & Scaling

Pythagoras and changing dimensions

What your child practices

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.

Alabama Course of Study content standard: GDA.19; GDA.36 · the Pythagorean Theorem in context, and how scaling changes lengths, areas and volumes

How we explain it

Children can open this short lesson before they practice.

  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

Right Triangles & Scaling in Alabama

In the Alabama Course of Study, this is unit 7 of 18 in 9th grade Math, after Similarity & Scale and before Right-Triangle Trig.

Gradelings describes a child's practice on this unit as Beginning, Approaching, Meeting or Exceeding (Four practice steps). That reflects practice, not a report-card mark: the teacher decides the mark.

Source: Alabama State Department of Education (ALSDE)

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 39 m ladder leans on a wall with its foot 15 m from the wall. How high up the wall does it reach, in meters?

    answer boxm

  2. Question 2

    Every edge of a cube is multiplied by 3. By what factor does the volume change?

    answer boxtimes

  3. Question 3

    A rectangle is 6 cm by 5 cm. Its width is multiplied by 4, and its height stays the same. What is the new area, in cm²?

    answer boxcm²

  4. Question 4

    A rectangular field is 7 m by 24 m. How long is its diagonal, in meters?

    answer boxm

  5. Question 5

    A ramp has a horizontal run of 20 m and a rise of 21 m. How long is the sloping surface, in meters?

    answer boxm

  6. Question 6

    A triangle has sides 10 cm, 24 cm and 26 cm. Is it a right triangle?

    • Yes, it is a right triangle
    • No, it is not a right triangle

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