length of opposing sides of isosceles triangle

[gcomish]

Given an isosceles triangle with a base of 12. A line horizontal to the base intersects the triangle. Its length is 8. How do I determine the length of the opposing sides? Is this enough info?

Sorry if this is so fundamental, but haven't used geometry for a long time. If you could provide steps, that would be great because the measurements might not be spot on.

Application: Trying to determine the radius of a circle necessary for encircling a tree with 12 inch pavers. The opposing side of the trapezoidal pavers is 8 inches.

 

[tkhunny]

"horizontal"? I think you mean "parallel".

In any case, think about "Similar Traingles". Corresponding parts of similar triangles are proportional.

If the base is 12 and the interescting parallel is 8, then the sides of the 8+ triangle will be 2/3 the side of the 12+ triangle.

If you do not know the length of the 12+ sides, you will have to provide more information. An angle? Something.

Your trapezoids are 8" toward the tree and 12" away from the tree? I continue to believe that you will need to know the last distance before you can figure it out. What's the width of the paver? This distance from the 12" side to the 8" side?

 

[mmm4444bot]

A line horizontal to the base I'm not sure what this phrase means. Perhaps, the line segment is parallel to the base.

encircling a tree with 12 inch pavers It's possible to form many differently-sized encirclings by placing pavers around a tree.

Hi gcomish:

Are you working with a fixed amount of materials, and you're trying to determine how large a circle you can form? Otherwise, it seems that you would first decide the size encircling that you desire, followed by calculating the number of pavers needed.

Are you designing the pavers? Are they to be placed snuggly together?

If the image below depicts what you're thinking about the triangle, then there is not enough information to determine the two equal sides.

I think we need more details about what you're trying to do. With trapezoidal pavers, I'm thinking that the finished object will be a polygon, not a circle. If this is the case, then maybe you need to decide how many sides you want. Eight sides (octogon)? Twelve sides (dodecagon)? As the number of sides increases, the distance between the 8-inch and 12-inch sides of the pavers gets shorter.

Can you describe in greater detail what you're trying to do. Are you able to upload some sketches?

Cheers,

~ Mark