Proportional Geometry Math Example 1

Follow the full solution, then compare it with the other examples linked below.

Example 1

easy
Two similar triangles have corresponding sides in the ratio 3:5. If the shorter triangle has a base of 9 cm, what is the base of the larger triangle?

Solution

  1. 1
    Step 1: Set up the proportion: short baselong base=35\dfrac{\text{short base}}{\text{long base}} = \dfrac{3}{5}.
  2. 2
    Step 2: 9x=35\dfrac{9}{x} = \dfrac{3}{5}.
  3. 3
    Step 3: Cross-multiply: 3x=45⇒x=153x = 45 \Rightarrow x = 15 cm.

Answer

15 cm
Similar figures have all corresponding lengths in the same ratio (the scale factor). Setting up a proportion and cross-multiplying is the standard method to find a missing length in similar figures.

About Proportional Geometry

Proportional geometry studies how corresponding lengths, areas, and volumes scale between similar figures. If two triangles are similar with scale factor k, their sides are in ratio k, their areas in ratio k², and their volumes in ratio k³.

Learn more about Proportional Geometry →

More Proportional Geometry Examples

Example 2 medium

A 6 ft tall person casts a shadow 4 ft long. At the same time, a tree casts a shadow 14 ft long. How

Example 3 medium

Two similar rectangles have widths [formula] cm and [formula] cm. If the smaller rectangle has lengt

Example 4 easy

Two similar rectangles have widths 5 cm and 15 cm. What is the scale factor from the smaller to the

Example 5 hard

On a map, 1 cm represents 50 km. Two cities are 3.6 cm apart on the map. What is the actual distance

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