1. ## Similar triangles

I have an equillateral triangle and require to calculate the lengths of two parallel lengths.

I have included a sketch to help identify.

BC = AB = AC
YZ AY AZ

I know;

AB = 3
AC = 3
AY = 2
AZ = 2

I require to find the ratios BC and YZ

AB = AC = BC
AZ AY YZ

3 = 3 = x
2 2 x

How do I work with this method above to isolate BC and YZ

2. ## Re: Similar triangles

Originally Posted by David Green
I have an equillateral triangle and require to calculate the lengths of two parallel lengths.
How do I work with this method above to isolate BC and YZ
Because $\displaystyle \Delta ABC \approx \Delta AYZ\, \Rightarrow \,\frac{{BC}}{{YZ}} = \frac{{BA}}{{YA}}$.

3. ## Re: Similar triangles

Originally Posted by Plato
Because $\displaystyle \Delta ABC \approx \Delta AYZ\, \Rightarrow \,\frac{{BC}}{{YZ}} = \frac{{BA}}{{YA}}$.
The problem there is that you have given two unknowns on the LHS, where both cannot be solved at the same time?

I know the answers, but I don't know how to perform the algebra to solve the lengths of the sides?

4. ## Re: Similar triangles

Originally Posted by David Green
The problem there is that you have given two unknowns on the LHS, where both cannot be solved at the same time? I know the answers, but I don't know how to perform the algebra to solve the lengths of the sides?
It is an equilateral triangle: $\displaystyle CB=BA=AC$

5. ## Re: Similar triangles

Originally Posted by Plato
It is an equilateral triangle: $\displaystyle CB=BA=AC$
I know its an equilateral triangle, and I know each angle is 60 degrees, and I know AB = 3, BC = 3, and AC = 3, and YZ = 2

I just can't prove it mathematically

6. ## Re: Similar triangles

Originally Posted by David Green
I know its an equilateral triangle, and I know each angle is 60 degrees, and I know AB = 3, BC = 3, and AC = 3, and YZ = 2

I just can't prove it mathematically
It's a given, you don't need to prove it. Unless you've mistyped the question

7. ## Re: Similar triangles

Originally Posted by david green
i know its an equilateral triangle, and i know each angle is 60 degrees, and i know ab = 3, bc = 3, and ac = 3, and yz = 2
i just can't prove it mathematically
Help!

8. ## Re: Similar triangles

Thanks for info.