Triangle A has an area of 3 3 and two sides of lengths 5 5 and 6 6. Triangle B is similar to triangle A and has a side with a length of 11 11. What are the maximum and minimum possible areas of triangle B?

1 Answer
May 11, 2018

Min Possible Area = 10.08310.083
Max Possible Area = 14.5214.52

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 5/11511.
When squared, (5/11)^2 = 25/121(511)2=25121 is the ratio related to Area.

To find the Area of Triangle B, setup a proportion:
25/121 = 3/(Area)25121=3Area
Cross Multiply and Solve for Area:
25(Area) = 3(121)25(Area)=3(121)
Area = 363/25 = 14.52Area=36325=14.52

If triangle A's side of 6 corresponds with triangle B's side of 11, it creates a ratio of 6/11611.
When squared, (6/11)^2 = 36/121(611)2=36121 is the ratio related to Area.

To find the Area of Triangle B, setup a proportion:
36/121 = 3/(Area)36121=3Area
Cross Multiply and Solve for Area:
36(Area) = 3(121)36(Area)=3(121)
Area = 363/36 = 10.083Area=36336=10.083

So Minimum Area would be 10.083
while Maximum Area would be 14.52