Question

Triangle A has an area of `6` and two sides of lengths `5` and `7`. Triangle B is similar to triangle A and has a side with a length of `19`. What are the maximum and minimum possible areas of triangle B?

Answer 1

Maximum area of triangle is 86.64 and Minimum area is **44.2041#

Explanation:

`Delta s A and B` are similar.

To get the maximum area of `Delta B`, side 19 of `Delta B` should correspond to side 5 of `Delta A`.

Sides are in the ratio 19 : 5
Hence the areas will be in the ratio of `19^2 : 5^2 = 361 : 25`

Maximum Area of triangle `B =( 6 * 361) / 25= 86.64`

Similarly to get the minimum area, side 7 of `Delta A` will correspond to side 19 of `Delta B`.
Sides are in the ratio `19 : 7` and areas `361 : 49`

Minimum area of `Delta B = (6*361)/49= 44.2041`