SOLUTION: Given: Angle A is the vertex of an isosceles triangle. The number of degrees in angle B is twice the number of centimeters in segment BC. The number of degrees in angle C is three

Question 1002463: Given: Angle A is the vertex of an isosceles triangle. The number of degrees in angle B is twice the number of centimeters in segment BC. The number of degrees in angle C is three times the number of centimeters in segment AB.
m angle b=x+6
m angle c=2x-54
Find: The perimeter of triangle ABC

At this point, I have no clue where to start. I've drawn the triangle with it's angles labeled but that's as much as I'm able to do.

Found 2 solutions by josgarithmetic, MathTherapy:
Answer by josgarithmetic(39625) (Show Source): You can put this solution on YOUR website!

A diagram made to show Triangle ABC, A at top, B and C as base angle points. AB=AC and as given angle measure at B is 2*BC, and angle measure at C is 3*AB. The base angles are congruent which is to mean measure angle at B equals measure of angle at C.

The two relationships:

Using that system of equations,

Goal is to find perimeter.

This seems the best that can be done. Something of this sort or another equivalent is what is possible. The problem description is not enough for a VALUE for the perimeter.
(POST-ADD: I believe misunderstood the data given AFTER the description, and did not use that as any data.)
Answer by MathTherapy(10555) (Show Source): You can put this solution on YOUR website!

Given: Angle A is the vertex of an isosceles triangle. The number of degrees in angle B is twice the number of centimeters in segment BC. The number of degrees in angle C is three times the number of centimeters in segment AB.
m angle b=x+6
m angle c=2x-54
Find: The perimeter of triangle ABC

At this point, I have no clue where to start. I've drawn the triangle with it's angles labeled but that's as much as I'm able to do.

Angle C = 2x � 54 (given)
Angle C = 3(AB)
2x � 54 = 3AB

Angle B = x + 6 (given)
Angle B = 2(BC)
x + 6 = 2BC

With A being the vertex angle, angle B = angle C, OR
x + 6 = 2x � 54
x � 2x = - 54 � 6
- x = - 60
x = 60

, or , or 22 cm
AC also = 22 cm
, or , or , or 33 cm
Perimeter: 2(22) + 33, or 44 + 33, or cm
RELATED QUESTIONS
An isosceles triangle has a base of 46 centimeters and a vertex angle of 44 degrees. what (answered by CharlesG2)
find the number of degrees in the vertex angle of an isosceles triangle if each base... (answered by drk)
the measure of a base angle of an isosceles triangle is 4 times the measure of the vertex (answered by stanbon)
A base angle of an isosceles triangle measures 50 degrees. Find the number of degrees in... (answered by RedemptiveMath)
A base angle if an isosceles triangle measures 50 degrees. Find the number of degrees in... (answered by Simnepi)
In isosceles triangle ABC, vertex angle B=94 degrees. what is the measure of each base... (answered by Mathtut)
A base angle of an isosceles triangle is 9 degrees more than the vertex angle. Find a... (answered by josgarithmetic,TeachMath)
the measure of the vertex angle of an isosceles triangle is 48 degrees. find the measure... (answered by rapaljer)
The vertex angle of an isosceles triangle is 64 degrees. find the measure of a base... (answered by jim_thompson5910)