# Can we find the perimeter of a triangle given only its base and height?

How do you find the perimeter of a triangle that you only have the base and height measurements for?

Please use ENGLISH and not difficult mathematical formulas! I understand little algebra so avoid it if you can. Thank you!

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You can't. The perimeter must be at least $b+\sqrt{b^2+4h^2}$, but can be made as large as you want, by putting the apex far away off to one side.

If you know that both angles at the base are acute, then the perimeter must be less than $b+h+\sqrt{b^2+h^2}$.

(I'm not sure whether you consider these to be "difficult mathematical formulas"? Alternative form: "Multiply the height with itself, multiply by four, and add the base multiplied by itself. Take the square root of the sum, and add the base. The result is the smallest possible perimeter.")

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Draw two triangles. Make both of them have base 1 and height 1. Make the first one a right-triangle (by putting the height at the end of the base), make the other by putting the height in the middle of the base. Can you calculate the two perimeters? If you can, you have an answer to your question.

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## protected by Zev ChonolesJul 26 '15 at 22:15

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