AI generatedGeometry and measuresKey Stage 3

Finding a missing length in similar shapes

Finding a missing length in similar shapes.

  • Match corresponding lengths before taking a ratio.
  • Length scale factor gives area factor and volume factor .
  • Reverse with a square root or cube root when an area or volume ratio is given.

Example 1

Find the missing length .

Two triangles with equal corresponding angles, not to scaleEqual corresponding angles; not to scale
Large corresponding length ÷ small corresponding length.Multiply the matching small length by the same scale factor.

Example 2

Find the missing length .

Two triangles with equal corresponding angles, not to scaleEqual corresponding angles; not to scale
Large corresponding length ÷ small corresponding length.Multiply the matching small length by the same scale factor.

Your turn

Question 1

Find the missing length .

Two triangles with equal corresponding angles, not to scaleEqual corresponding angles; not to scale
Check answer
Large corresponding length ÷ small corresponding length.Multiply the matching small length by the same scale factor.
Question 2

Find the missing length .

Two triangles with equal corresponding angles, not to scaleEqual corresponding angles; not to scale
Check answer
Large corresponding length ÷ small corresponding length.Multiply the matching small length by the same scale factor.
Question 3

Find the missing length .

Two triangles with equal corresponding angles, not to scaleEqual corresponding angles; not to scale
Check answer
Large corresponding length ÷ small corresponding length.Multiply the matching small length by the same scale factor.
Question 4

Find the missing length .

Two triangles with equal corresponding angles, not to scaleEqual corresponding angles; not to scale
Check answer
Large corresponding length ÷ small corresponding length.Multiply the matching small length by the same scale factor.
Question 5

Find the missing length .

Two triangles with equal corresponding angles, not to scaleEqual corresponding angles; not to scale
Check answer
Large corresponding length ÷ small corresponding length.Multiply the matching small length by the same scale factor.
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