Question

Triangle A has an area of `5` and two sides of lengths `4` and `7`. Triangle B is similar to triangle A and has a side of length `18`. What are the maximum and minimum possible areas of triangle B?

Answer 1

Maximum possible area of triangle B = 101.25
Minimum possible area of triangle B = 33.0612

Explanation:

`Delta s A and B` are similar.

To get the maximum area of `Delta B`, side 18 of `Delta B` should correspond to side 4 of `Delta A`.

Sides are in the ratio 18 : 4
Hence the areas will be in the ratio of `18^2 : 4^2 = 324 : 16`

Maximum Area of triangle `B =( 5 * 324) / 16= 101.25`

Similarly to get the minimum area, side 7 of `Delta A` will correspond to side 18 of `Delta B`.
Sides are in the ratio `18 : 7` and areas `324 : 49`

Minimum area of `Delta B = (5*324)/49= 33.0612`