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Similarity
Similar solids

A pair of three-dimensional figures is classified as similar solids when they are the same shape and their corresponding measurements are proportional. The ratio that compares the measurements of two similar solids is called the scale factor.

The figures below are similar. What is p?

Remember that corresponding lengths of similar figures are proportional.
One pair of corresponding lengths is 8 mm and 6 mm. Another pair of corresponding lengths is 8 mm and p. Use these two pairs of corresponding lengths to set up a proportion and solve for p.

 8 6
=
 8 p
Plug in the pairs of corresponding lengths

8p  =  8 × 6 Find the cross products

8p  =  48 Simplify

8c ÷ 8  =  48 ÷ 8 Divide both sides by 8

p  =  6

The missing length is 6 millimetres.

The figures below are similar. What is w?

Remember that corresponding lengths of similar figures are proportional.
One pair of corresponding lengths is 2 mm and 4 mm. Another pair of corresponding lengths is w mm and 16.

Use these two pairs of corresponding lengths to set up a proportion and solve for w.

 2 4
=
 w 16
Plug in the pairs of corresponding lengths

4w  =  2 × 16 Find the cross products

w  =  32 ÷ 4 Simplify

w  =  8

The missing length is 8 centimetres.