# 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?

##### 1 Answer

By the square of

#### Explanation:

We know that triangle A has fixed internal angles with the given information. Right now we are only interested in the **angle between lengths #8&15#.**

That angle is in the relationship:

Hence:

With that angle, we can now find the **length of the third arm of**

From **longest and shortest arms are 15 and 8 respectively.**

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.**

A similar **largest possible** hence **Minimum possible area** if

Therefore maximum area of B is **54** and the minimum area is **15.36**.