Question

Triangle A has an area of `7` and two sides of lengths `4` and `9`. Triangle B is similar to triangle A and has a side with a length of `7`. What are the maximum and minimum possible areas of triangle B?

Answer 1

Maximum area 21.4375 and Minimum area 4.2346

Explanation:

`Delta s A and B` are similar.

To get the maximum area of `Delta B`, side 7 of `Delta B` should correspond to side 4 of `Delta A`.

Sides are in the ratio 7 : 4
Hence the areas will be in the ratio of `7^2 : 4^2 = 49 : 16`

Maximum Area of triangle `B =( 7 * 49 / 16= 21.4375`

Similarly to get the minimum area, side 9 of `Delta A` will correspond to side 7 of `Delta B`.
Sides are in the ratio `7 : 9` and areas `49 : 81`

Minimum area of `Delta B = (7*49)/81= 4.2346`