Triangle A has an area of #24 # and two sides of lengths #8 # and #15 #. Triangle B is similar to triangle A and has a side with a length of #12 #. What are the maximum and minimum possible areas of triangle B?
By the square of
We know that triangle A has fixed internal angles with the given information. Right now we are only interested in the angle between lengths
That angle is in the relationship:
With that angle, we can now find the length of the third arm of
Similar triangles will have their ratios of arms extended or contracted by a fixed ratio. If one arm doubles in length, the other arms double as well . For area of a similar triangle, if the length of arms double, the area is a size bigger by a factor of 4.
Therefore maximum area of B is 54 and the minimum area is 15.36.