Question

Triangle A has an area of `18` and two sides of lengths `8` and `12`. Triangle B is similar to triangle A and has a side of length `8`. What are the maximum and minimum possible areas of triangle B?

Answer 1

Maximum possible area of triangle B = 18
Minimum possible area of triangle B = 8

Explanation:

`Delta s A and B` are similar.

To get the maximum area of `Delta B`, side 8 of `Delta B` should correspond to side 8 of `Delta A`.

Sides are in the ratio 8 : 8
Hence the areas will be in the ratio of `8^2 : 8^2 = 64 : 64`

Maximum Area of triangle `B =( 18 * 64) / 64= 18`

Similarly to get the minimum area, side 12 of `Delta A` will correspond to side 8 of `Delta B`.
Sides are in the ratio `8 : 12` and areas `64 : 144`

Minimum area of `Delta B = (18*64)/144= 8`