Practice Maths

Applications of Pythagoras’ Theorem — Solutions

Click any answer to watch the solution video.

  1. Converse of Pythagoras

    1. 6, 8, 10:
    2. 5, 7, 9:
    3. 9, 40, 41:
    4. 4, 5, 6:
    5. 11, 60, 61:
    6. 8, 10, 13:
    7. 20, 21, 29:
    8. 3, 4, 6:

  2. Distance on a coordinate plane

    1. A(0,0) and B(5,12):
    2. P(2,3) and Q(6,6):
    3. M(−3,1) and N(1,4):
    4. S(4,−2) and T(4,7):
    5. X(−1,−2) and Y(3,1):

  3. 3D diagonals

    1. 3, 4, 12:
    2. 6, 6, 7:
    3. 2, 3, 6:
    4. Cube 4×4×4:

  4. Real-world applications

    1. Ladder 6m, foot 1.5m from wall:
    2. 12km north, 5km west:
    3. Square diagonal 200m:
    4. Shadow 30m, cable 50m:

  5. Reasoning with Pythagoras

    1. Sides 2√3, 4, 2√7:
    2. A(1,2) B(7,k), AB=10:
    3. Square diagonal 10cm:
    4. Diagonal of square side s:

  6. Extended problem solving

    1. Pole 8m, cables from 6m and 15m:
    2. Van 2.4×1.6×1.8, pole 4.5m:
    3. Triangle A(0,0) B(4,0) C(0,3):
    4. Pool 25m×10m:

  7. Reasoning with Pythagoras

  8. 3D space diagonals

    1. 3×4×12 m:
    2. 2×3×6 m:
    3. 4×4×4 cm (cube):
    4. 6×6×7 cm:

  9. Pole cables and fitting a rod

  10. Coordinate geometry: triangle and altitude