# Triangle A has an area of 8  and two sides of lengths 8  and 7 . Triangle B is similar to triangle A and has a side with a length of 16 . What are the maximum and minimum possible areas of triangle B?

Maximum Area $= 361.28 \text{ }$square units
Minimum Area $= 9.29514 \text{ }$square units

#### Explanation:

I computed all possible triangles and there are 2 possible triangles for A and 6 possible triangles for B. Then I computed the area for each triangle to determine the maximum and minimum areas.

For first triangle A:
sides $a = 8$ , $b = 7$ , $c = 2.3809 \text{ }$,angle $C = {16.6015}^{\circ}$

For first triangle B:
sides $a ' = 16$, $\text{ } b ' = 14$, $\text{ } c ' = 4.76182$,angle $C = {16.6015}^{\circ}$,
Area$= 32$

sides $a ' ' = \frac{128}{7}$,$\text{ } b ' ' = 16$, $\text{ } c ' ' = 5.44208$,angle $C = {16.6015}^{\circ}$,
Area$= 41.7959$

sides $a ' ' ' = 53.7609$,$\text{ } b ' ' ' = 47.0408$,$\text{ } c ' ' ' = 16$,angle $C = {16.6015}^{\circ}$,
Area$= 361.28 \text{ }$Maximum Area
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For second triangle A:
sides $a = 8$ , $b = 7$ , $c = 14.8436 \text{ }$,angle $C = {163.398}^{\circ}$

For first triangle B:
sides $a ' = 16$, $\text{ } b ' = 14$, $\text{ } c ' = 29.6871$,angle $C = {163.398}^{\circ}$,
Area$= 32$

sides $a ' ' = \frac{128}{7}$,$\text{ } b ' ' = 16$, $\text{ } c ' ' = 33.9281$,
angle $C = {163.398}^{\circ}$,
Area$= 41.798$

sides $a ' ' ' = 8.62327$,$\text{ } b ' ' ' = 7.54536$,$\text{ } c ' ' ' = 16$,
angle $C = {163.398}^{\circ}$,
Area$= 9.29514 \text{ }$Minimum Area

God bless....I hope the explanation is useful.