National 5 Maths worked question

Find a ladder length using Pythagoras

A fixed, reviewed pythagoras question with a complete worked solution and method explanation.

Standard3 marksCalculator optional

Question

A ladder reaches 4.8 m up a vertical wall. Its foot is 1.4 m from the wall. Calculate the length of the ladder.

Show the worked solution

Worked solution

  1. The wall, ground and ladder form a right-angled triangle.

    The ladder is opposite the right angle, so it is the hypotenuse.

  2. l² = 4.8² + 1.4²

    Use Pythagoras with the two shorter sides.

  3. l² = 23.04 + 1.96 = 25

  4. l = √25 = 5

    Take the positive square root because a length is positive.

Final answer: The ladder is 5 m long.

Why this method works

Pythagoras connects the three side lengths of a right-angled triangle. Because the ladder is the hypotenuse, add the squares of the two perpendicular shorter sides before taking the square root.

Check your work

Check that the ladder is longer than both 4.8 m and 1.4 m. A result of 5 m is sensible.

Common mistakes

  • Treating 4.8 m as the hypotenuse.
  • Adding the side lengths before squaring them.
  • Forgetting to take the square root after finding l²