SOLUTION: The longest side of a triangle is 16 less than the sum of the other two. The shortest side is three times the difference of the other two. The Perimeter is 150. Write the system of

Question 491280: The longest side of a triangle is 16 less than the sum of the other two. The shortest side is three times the difference of the other two. The Perimeter is 150. Write the system of equation.
Answer by cleomenius(959) (Show Source): You can put this solution on YOUR website!
Let
a = longest
b = middle
c = smallest
=========================================================
Set up our equations.
-a +b + c = 16
3a - 3b -c = 0
a + b + c = 150
=======================================================
multiply 1 * 3;add 1 to 2
-a +b + c = 16
2c = 48
a + b + c = 150
c = 24
=============================================
plug c into 1 and 3,
-a +b + 24= 16
2c = 48
a + b + 24= 150
multiply 1 by -1, add 1 to 3
-a +b + 24= 16
2c = 48
2a + 0= 134
a = 67 degrees.
========================================================
Solve for b.
67 + 24 = 91 ; 150 - 91 = 59
b = 59 degrees.
=======================================================
a = 67 degrees.
b = 59 degrees.
c = 24 degrees.
Now, to check the system.
59 + 24 = 83; 83 - 16 = 67.
67 - 59 = 8; 8*3 = 24, which is the smallest angle.
67 + 59 + 24 = 150.
This system does check.
Cleomenius.

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