Similar Figures 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 66 cm and 1010 cm. If the smaller triangle has a perimeter of 2121 cm, find the perimeter of the larger triangle.

Solution

  1. 1
    Scale factor (larger to smaller): k=106=53k = \dfrac{10}{6} = \dfrac{5}{3}.
  2. 2
    Perimeters of similar figures scale by the same ratio as corresponding sides.
  3. 3
    Perimeter of larger triangle =21×53=35= 21 \times \dfrac{5}{3} = 35 cm.

Answer

The larger triangle has perimeter 3535 cm.
All linear measurements in similar figures scale by the same ratio kk. Only areas scale by k2k^2 and volumes by k3k^3. Once the scale factor is identified from one pair of corresponding sides, all other proportions follow.

About Similar Figures

Similar figures have the same shape with corresponding angles equal and corresponding sides proportional.

Learn more about Similar Figures →

More Similar Figures Examples

Example 2 hard

Rectangle [formula] Rectangle [formula] with [formula], [formula], [formula]. Find [formula] and the

Example 3 easy

Triangle [formula] Triangle [formula]. [formula], [formula], [formula]. Find [formula].

Example 4 medium

Two similar cones have base radii [formula] cm and [formula] cm. What is the ratio of their volumes?

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