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These are the plans for a vegetable garden that a school is designing.
Scale: 1 unit = 2.8 ft
Write at least 3 equivalent ratios or equations using lengths from both the diagram and the full-size garden.
Your teacher will give you a set of cards. Group them into pairs of similar figures. For each pair, determine:
a similarity statement.
the scale factor between the similar figures.
the missing lengths.
Here is a quilt design made of right isosceles triangles. The smallest squares in the center have an area of 1 square unit.
Find the dimensions of the triangles.
When two figures are similar, there are lots of equivalent ratios between the triangles and within the triangles. We can use those relationships to find missing lengths. For example, if we know that triangle is similar to triangle , we know that pairs of corresponding side lengths are in the same proportion.
We also know that pairs of side lengths in one triangle are in the same proportion as pairs of side lengths in the other triangle.
We can use these equivalent ratios to find unknown side lengths. Which equivalent ratios would work to find ?
We can use to find . Then , which gives .
Or we can use to find . In this case, we get , which also gives .