geometry
I have a question where the teacher wants me to find the perimeter of a right triangle using the area which is equal to $1cm^2$. I've tried a few approaches but seem to be struggling and I can't even find the side lengths. is this even possible?
would love some help thanks
From the Wikipedia article on Thales' theorem:
If you know the hypotenuse, you know the base of this diagram; if you also know the area, then you can compute the height (from $A=\frac12 bh$). Then you can draw a horizontal line at the required height; where it intersects the circle is the vertex with the right angle.
Best Answer
If that is all the information you have, you can't find the perimeter. If the triangle is isosceles and the leg is $x$, the area is $\frac {x^2}2$, so $x=\sqrt 2$ and the perimeter is $2\sqrt 2+2$. If the triangle has a very long leg $L$ and a short leg of length $x$, the area is $\frac 12xL$, so $L=\frac 2x$. The perimeter is then $x+L+\sqrt{x^2+L^2}\approx 2L$ which can be as large as you like.