Hi -

I'm not quite sure what the problem is that you have in visualising this. You simply take a straight piece of wire and bend it into a right-angle somewhere along its length!

Nothing more than that. The two parts of the wire are now at right-angles to one another. So they form the two shorter sides of a right-angled triangle. An imaginary line joining the two ends of the wire forms the hypotenuse of the triangle.

To solve the problem, let's suppose that the 20cm length is now divided into two parts, one of length x cm and the other of length (20 - x) cm.

Then use the area formula Area = (half base times height) to work out the area in terms of x. Put the answer equal to 30, and you will have a quadratic equation in x. Solve this, and you can work out the length of the hypotenuse and the perimeter.

I hope that helps.

Grandad