Triangle A has an area of #12 # and two sides of lengths #6 # and #9 #. Triangle B is similar to triangle A and has a side of length #15 #. What are the maximum and minimum possible areas of triangle B?
2 Answers
Maximum area of
Minimum area of
Explanation:
Similar triangles have identical angles and size ratios. That means the change in length of any side either larger or smaller will be the same for the other two sides. As a result, the area of the
It has been shown that if the ratio of the sides of similar triangles is R, then the ratio of the areas of the triangles is
Example: For a
But if all three sides are doubled in length, the area of the new triangle is
From the information given, we need to find the areas of two new triangles whose sides are increased from either
Here we have
We also have larger
The ratio of the change in area of
The ratio of the change in area of
The minimum is
Explanation:
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Because the two triangles are similar, call them triangle
Start by recalling Heron's theorem
We can now use this information to find the areas. If