SOLUTION: the first side of the triangle is 4 cm longer than the second side. the third side is 3 times the second side. The perimeter is 44cm. how long is each side

Question 1136737: the first side of the triangle is 4 cm longer than the second side. the third side is 3 times the second side. The perimeter is 44cm. how long is each side
Found 4 solutions by Boreal, MathTherapy, ikleyn, Alan3354:
Answer by Boreal(15235)   (Show Source): You can put this solution on YOUR website!
perimeter=44=sum of sides
second is x
first is x+4
third is 3x
so x+x+4+3x=44
5x+4=44
5x=40
x=8 cm for second
12 cm for first
24 cm for third
Answer by MathTherapy(10552)   (Show Source): You can put this solution on YOUR website!
the first side of the triangle is 4 cm longer than the second side. the third side is 3 times the second side. The perimeter is 44cm. how long is each side

While solving this results in sides of 8 cm, 12 cm, and 24 cm, I must point out that such a triangle is IMPOSSIBLE to construct.
People need to do a much better job of forming these math problems. If a child who has yet to learn certain things made up such a problem,
I'd understand, but I'd also show he/she why certain NONSENSICAL problems should be avoided.
When 2 of the lines are constructed, the 3rd will either be TOO SHORT to close the triangle, or TOO LONG, thereby extending one side beyond the CLOSING point.
Answer by ikleyn(52803)   (Show Source): You can put this solution on YOUR website!
.

The tutor @Boreal correctly determined the side lengths from the condition: they are 8 cm, 12 cm and 24 cm.

But he missed to check, if such a triangle may exist.

Actually (and factually), there is NO triangle with such side lengths, since it contradicts to the triangle inequality

            a + b > c

which must be true for any combination of sides of any triangle.

In our case

            8 + 12 = 20 < 24

and the triangle inequality fails.

It is a simple rule, and I repeated it many times in my posts to this forum:

when you solve a problem, where you need to determine the side lengths of a triangle, you MUST check at the end of your solution, whether the triangle inequalities are satisfied. Without doing it, you can make a HUGE mistake.

It is the major lesson to learn from my post.

Answer by Alan3354(69443)   (Show Source): You can put this solution on YOUR website!
this is not possible for a triangle in a plane.
I doubt it was intended to be a spherical triangle.

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