Triangle A has an area of #3 # and two sides of lengths #5 # and #6 #. Triangle B is similar to triangle A and has a side with a length of #11 #. What are the maximum and minimum possible areas of triangle B?
1 Answer
Min Possible Area =
Max Possible Area =
Explanation:
When two objects are similar, their corresponding sides form a ratio. If we square the ratio, we get the ratio related to area.
If triangle A's side of 5 corresponds with triangle B's side of 11, it creates a ratio of
When squared,
To find the Area of Triangle B, setup a proportion:
Cross Multiply and Solve for Area:
If triangle A's side of 6 corresponds with triangle B's side of 11, it creates a ratio of
When squared,
To find the Area of Triangle B, setup a proportion:
Cross Multiply and Solve for Area:
So Minimum Area would be 10.083
while Maximum Area would be 14.52