2 Geometry questions. 10 points (Triangles)

1. The measures of the sides of an equilateral triangle are represented by x + 12, 3x - 8, and 2x + 2. What is the measure of each side of the triangle?

2. The measures of the sides of an isosceles triangle are represented by 2x + 5, 2x - 6, and 3x - 3. What are the lengths of the sides of the triangle? (Hint: The length of a line segment is a positive quantity).

Need help on those 2 questions please. 10 points for best answer

1. Since the triangle is equilateral, the three sides of the triangle are equal in length.

So just take any two sides, equate them, then solve for x

x + 12 = 3x - 8 for example

Then isolate the terms:

12 + 8 = 3x - x

20 = 2x

x = 10

Now just plug 10 back into the three expressions

The first side is 10 + 12 which is 22, the second side is 3(10) - 8 which is 22, and the last side is 2(10) + 2 = 22.

DONE.

2. The same approach, except this time a little more complicated. You have to do step 1 in the previous question till you get a positive value for the expression. I bet you did not understand what I just said, but just bear it in mind. You will get it later on.

So, it is isosceles. This means two sides are equal. How do you know which two sides though? Well, you just have to try em out.

Let's say the first two sides are equal.

2x + 5 = 2x - 6

2x - 2x = -11

WAIT WHAT? That doesn't make sense. This means the first two sides are not the two equal ones.

Try the next two.

2x - 6 = 3x - 3

-3 = 5x

x = -3/5

So this time you get an answer but what happens when you put x = -3/5 back into the expression, you get 2(-3/5) - 6 which is -13. WTF how can a side of a triangle be negative?

So that's not right either. You end up with the 1st and 3rd one. Those two are the two equal ones.

2x + 5 = 3x - 3

8 = x

Substitute the x = 8 back into the expressions and you get 2(8) + 5 which is 21, 2(8) - 6 which is 10, and 3(8) - 3 = 21. You see that the 1st and 3rd sides are indeed equal.