The base and height both increase by x feet \(\left(x>0\right)\).We have :

\(\dfrac{\left(x+3\right)\left(x+6\right)}{2}=35\)\(\Leftrightarrow x^2+9x+18=70\)

\(\Leftrightarrow x^2+9x-52=0\)\(\Rightarrow\left[{}\begin{matrix}x=\dfrac{-9+\sqrt{81+4.52}}{2}=4\\x=\dfrac{-9-\sqrt{81-4.52}}{2}=-13\end{matrix}\right.\)

Since x > 0, x = 4 and x + 3 = 7 ; x + 6 = 10

Hence,the answer is : 7 + 10 = 17 (feet)