SOLUTION: if the measures of angles of an triangle in the ratio of 1:2:3, and if the perimeter of the triangle is 30 + 10 sqrt(3), what is the length of the smallest side ?

Question 328006: if the measures of angles of an triangle in the ratio of 1:2:3, and if the perimeter of the triangle is 30 + 10 sqrt(3), what is the length of the smallest side ?
Answer by rapaljer(4671) (Show Source): You can put this solution on YOUR website!
If the angles are in a ratio of 1:2:3, then let x = smallest angle.

The other angles are 2x and 3x respectively, so
x + 2x + 3x=180
6x=180
x=30
2x=60
3x=90

This is a 30-60-90 triangle, so the sides are in a ratio of 1:2:.

Let y= first side
2y= second side (hypotenuse of right triangle!)
= third side

Perimeter=

Therefore, y=10.
The smallest side is 10, the second side is 20, and the third side is . The perimeter checks!!

For additional help on GEOMETRY, please see my own website. Click on my tutorname "rapaljer" anywhere in algebra.com, and look for "Topics from Geometry" near the bottom of the page.
Dr. Robert J. Rapalje, Retired
Seminole State College of Florida
Altamonte Springs Campus

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