Answer
$45\ m$ by $90\ m$
Work Step by Step
Step 1. There are only three sides of the rectangle, let $x$ be the length of the two equal opposite sides, the third side will have a length of $180-2x$.
Step 2. The area is given by $A=x(180-2x)=-2(x^2-90x)$
Step 3. The maximum will happen when $x=-\frac{-90}{2}=45$
Step 4. Thus the dimensions are $45\ m$ by $90\ m$
