Question

Triangle A has an area of `4` and two sides of lengths `12` and `7`. Triangle B is similar to triangle A and has a side with a length of `5`. What are the maximum and minimum possible areas of triangle B?

Answer 1

Maximum possible area of triangle B = 2.0408
Minimum possible area of triangle B = 0.6944

Explanation:

`Delta s A and B` are similar.

To get the maximum area of `Delta B`, side 5 of `Delta B` should correspond to side 7 of `Delta A`.

Sides are in the ratio 5 : 7
Hence the areas will be in the ratio of `5^2 : 7^2 = 25 : 49`

Maximum Area of triangle `B =( 4 * 25) / 49= 2.0408`

Similarly to get the minimum area, side 12 of `Delta A` will correspond to side 5 of `Delta B`.
Sides are in the ratio `5 : 12` and areas `25 : 144`

Minimum area of `Delta B = (4*25)/144= 0.6944`