Question

Triangle A has an area of `12` and two sides of lengths `5` and `7`. Triangle B is similar to triangle A and has a side with a length of `19`. What are the maximum and minimum possible areas of triangle B?

Answer 1

Maximum Area `=187.947" "`square units
Minimum Area `=88.4082" "`square units

Explanation:

The triangles A and B are similar. By ratio and proportion method of solution, triangle B has three possible triangles.

For Triangle A: the sides are

`x=7`, `y=5`, `z=4.800941906394`,Angle `Z=43.29180759327^@`

The angle Z between sides x and y was obtained using the formula for area of triangle

`Area=1/2*x*y*sin Z`

`12=1/2*7*5*sin Z`

`Z=43.29180759327^@`

Three possible triangles for Triangle B: the sides are

Triangle 1.
`x_1=19`, `y_1=95/7`,`z_1=13.031128031641`,
Angle `Z_1=43.29180759327^@`

Triangle 2.
`x_2=133/5`,`y_2=19`, `z_2=18.243579244297`,
Angle `Z_2=43.29180759327^@`

Triangle 3.
`x_3=27.702897180004`, `y_3=19.787783700002`,
Angle `Z_3=43.29180759327^@`

Maximum Area with Triangle 3.
Minimum Area with Triangle 1.

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