How do you find a missing length in a triangle? I have two triangles. The lengths given are 18:27:x and the other one is 14:21:28.
I don't understand the question. You have only one missing length for two triangles?
I do note that the ratio of sides in the two cases is
2:3:(1/3)x
2:3:4
Just considering triangle 1, x could be anything less than 45 (bonus question: why?).
Maybe you want x so that the two triangles will be the same shape - same angles. If so, I think I've given you a big clue by writing the ratios of sides.
Perfect. I figured out what x was but I couldn't figure out how to show the calculations! The answer is 36, I think? Do you get the same thing?
Yes, absolutely!
Try this:
18 : 27 : x = 2*9 : 3*9 : x
14 : 21 : 28 = 2*7 : 3*7 : 4*7
Clearer now?
Yes, perfectly. Thank you. Sorry I wasn't clearer on my question asking
To find a missing side length in a triangle, we can use the concept of similar triangles. Similar triangles have proportional sides, meaning that the ratio of corresponding side lengths is the same.
Let's start with the first triangle that has side lengths 18, 27, and x. We can set up a proportion by comparing the corresponding side lengths of the two triangles:
18 / 14 = 27 / 21 = x / 28
To find the missing length x, we can solve the proportion. Cross-multiplying and simplifying, we get:
18 * 21 = 27 * 14
378 = 378
The proportion is consistent, indicating that the second triangle is a multiple of the first triangle. Since the side lengths of the first triangle are all multiplied by 2, we can apply the same multiplication factor to the second triangle to find the missing side length:
x = 28 * 2 = 56
Therefore, the missing side length in the first triangle is 56.