SOLUTION: The two sides of the triangle ABC has sides AB=22cm and AC=8. If the area of the triangle 34.98 cm�, what is it's perimeter?

Question 1129377: The two sides of the triangle ABC has sides AB=22cm and AC=8. If the area of the triangle 34.98 cm�, what is it's perimeter?
Found 2 solutions by ikleyn, MathLover1:
Answer by ikleyn(52803)   (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 cm�, what is it's perimeter?
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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,

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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.

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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,

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