GB-36-06-001 · Area and length scale factors
Two similar shapes have areas 1472 cm² and 7452 cm². Their smaller and larger perimeters are P and Q. Find Q : P in its simplest form.
Similar Shapes: L.A.V Table (Area to Perimeter Ratio)
Booklet p. 41
Method
1) Put corresponding measurements in an L.A.V table (or L.L for two lengths)
2) Length factor r, area factor r², volume factor r³
3) Multiply from small to large; divide in reverse
Worked Example (GB-36-06-001)
1)
| Dimension | Small | Scale factor: small → large | Large |
|---|---|---|---|
| A | 1472 | 7452 | |
| L / perimeter | P | Q |
2)
Perimeters scale like lengths, so . Simplify this ratio.
Ans =
9 : 4