The new dimensions are $15$ and $14$.
Work Step by Step
Our equation is according to the text of the exercise: $0.5\cdot21\cdot20=(21-x)(20-x)\\210=420+x^2-41x\\x^2-41x+210=0\\(x-35)(x-6)=0$ Thus $x=35$ or $x=6$ but $x$ has to be positive and less than $20$. Thus $x=6$. Thus the new dimensions are $15$ and $14$.