AI generatedGeometry and measuresGCSE Higher / IGCSE Extended

Deciding whether an area ratio or length ratio is required

Deciding whether an area ratio or length ratio is required.

  • Give a mathematical reason for each step.
  • Use matching angles and corresponding sides, not the appearance of a diagram.
  • State the result you have proved at the end.

Example 1

Two similar shapes have length ratio . Find the area ratio.

Square for areas; cube for volumes.

Example 2

Two similar shapes have area ratio . Find the length ratio.

Take the matching root to return to lengths.

Your turn

Question 1

Two similar shapes have length ratio . Find the area ratio.

Check answer
Square for areas; cube for volumes.
Question 2

Two similar shapes have area ratio . Find the length ratio.

Check answer
Take the matching root to return to lengths.
Question 3

Two similar shapes have length ratio . Find the area ratio.

Check answer
Square for areas; cube for volumes.
Question 4

Two similar shapes have area ratio . Find the length ratio.

Check answer
Take the matching root to return to lengths.
Question 5

Two similar shapes have length ratio . Find the area ratio.

Check answer
Square for areas; cube for volumes.