# Triangle A has an area of #4 # and two sides of lengths #6 # and #4 #. Triangle B is similar to triangle A and has a side with a length of #9 #. What are the maximum and minimum possible areas of triangle B?

##### 1 Answer

#### Explanation:

Let the areas of triangles be A1 & A2 and sides a1 & a2.

Condition for the triangle’s third side: Sum of the two sides must be greater than the third side.

In our case the given two sides are 6, 4.

Third side should be **less than 10 and greater than 2**.

Hence the third side will have the maximum value **9.9** and the minimum value **2.1**. (Corrected upto one decimal point)

Areas will be proportional to the (side)^2.

Case : Minimum Area :

When the similar triangle’s side 9 corresponds to 9.9, we get he Minimum area of the triangle.

Case : Maximum Area :

When the similar triangle’s side 9 corresponds to 2.1, we get he Maximum area of the triangle.