SOLUTION: A triangle has angle measures A= (12x-9), B= (62-3x), and C= (16x+2). Determine the longest sides of the triangle.

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Question 1150770: A triangle has angle measures A= (12x-9), B= (62-3x), and C= (16x+2). Determine the longest sides of the triangle.
Found 3 solutions by ikleyn, MathLover1, Alan3354:
Answer by ikleyn(52752) About Me  (Show Source):
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The longest side of a triangle is the side opposite to the largest angle.


So, let's determine the angles first.


    (12x-9) + (62-3x) + (16x+2) = 180°

    (12x - 3x + 16x) + (-9 + 62 + 2) = 180

     25x + 55 = 180

     25x = 180 - 55 

     25x = 125

       x = 125/25 = 5


The angles are:  A = 12*5-9 = 51°;  B = 62-3*5 = 47°;  C = 16*5+2 = 82°.


The longest side is AB.       ANSWER


Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!

A triangle has angle measures:
+A=+%2812x-9%29
B=+%2862-3x%29 and
C=+%2816x%2B2%29
first determine the measure of each angle
as you know, the sum of all angles in triangle is 180°
so, %2812x-9%29%2B%2862-3x%29%2B%2816x%2B2%29=180°...solve for x
12x-9%2B62-3x%2B16x%2B2=180°
25x%2B55=180°
25x=180-55°
25x=125°
x=125%2F25°
x=5°
now find the measure of each angle:
+A=+%2812x-9%29=>+A=+%2812%2A5-9%29=>+A=+51°
B=+%2862-3x%29=> B=+%2862-3%2A5%29=> B=+47°
C=+%2816x%2B2%29=> C=+%2816%2A5%2B2%29=> C=+82°=> the largest angle

Determine the longest sides of the triangle.
recall, the longest side in a triangle is opposite the largest angle; so, the longest sides of the triangle is side c

Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
A triangle has angle measures A= (12x-9), B= (62-3x), and C= (16x+2). Determine the longest sides of the triangle.
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The sum of the angles is 180 degs
Add them, solve for x.
etc
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the "longest sides" 2 of them? 3 of them?