|
Question 1129377: The two sides of the triangle ABC has sides AB=22cm and AC=8. If the area of the triangle 34.98 cm², what is it's perimeter?
Found 2 solutions by ikleyn, MathLover1:
Answer by ikleyn(52879)   (Show Source):
You can put this solution on YOUR website! .
     Triangle ABC has sides AB=22cm and AC=8. If the area of the triangle 34.98 cm², what is it's perimeter?
~~~~~~~~~~~~~~~~~~~
Use the formula
Area =  for the area of a triangle,
where "a" and "b" are two sides lengths and  is the angle between them.
Using given data, find  .
Having , find  = +/- .
===---> > > Notice that there is NO NEED to find : all you need is . < < <---===
Then find the length of the third side using the cosine law.
Then find the perimeter,
---------------
By the way, since may have (and factually has (!)) TWO values at given , you will have
TWO possible values for the third side, and, correspondingly, TWO values for the possible perimeter.
---------------
Regrading the solution by the tutor @Mathlover1, keep in mind that she loss one possible answer and makes
a lot of unnecessary calculations on her way (like finding ).
Answer by MathLover1(20850)  (Show Source):
You can put this solution on YOUR website! the triangle  has sides:
and 
If the area of the triangle and , we have
find  -> note that  divides triangle in two right triangles and side in two parts  and 
since we know  , ,
use Pythagorean theorem to find
then,  ->
now use Pythagorean theorem to find
, and 
what is it's perimeter?
or, this way:
Use the formula
 for the area of a triangle,
where "a" and "b" are two sides lengths and is the angle between them.
Using given data, find .
 °
Having  , find .
Then find the length of the third side using the cosine law.
Then find the perimeter,
|
|
|
| |
