Proportional Geometry Math Example 3

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

Example 3

medium
Two similar rectangles have widths 44 cm and 1010 cm. If the smaller rectangle has length 66 cm, find the length of the larger rectangle.

Solution

  1. 1
    Step 1: Find the scale factor from the smaller to the larger rectangle: k=104=52k = \dfrac{10}{4} = \dfrac{5}{2}.
  2. 2
    Step 2: Since the rectangles are similar, all corresponding lengths are in the same ratio. Set up the proportion: larger lengthsmaller length=k\dfrac{\text{larger length}}{\text{smaller length}} = k, so L=6×52L = 6 \times \dfrac{5}{2}.
  3. 3
    Step 3: Compute: L=302=15L = \dfrac{30}{2} = 15 cm.

Answer

The larger rectangle has length 1515 cm.
In similar figures, every pair of corresponding linear dimensions shares the same scale factor. Once you determine the scale factor from one pair of corresponding sides (the widths), you can multiply any dimension of the smaller figure by that factor to find the corresponding dimension in the larger figure.

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 1 easy

Two similar triangles have corresponding sides in the ratio 3:5. If the shorter triangle has a base

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 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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