Answer
$(x-5) \text{ centimeters}$
Work Step by Step
Using $A=bh$ or the forumula for the area of a parallelogram, then
\begin{array}{l}\require{cancel}
A=bh
\\\\
2x^2-17x+35=(2x-7)h
\\\\
\dfrac{2x^2-17x+35}{2x-7}=h
\\\\
h=\dfrac{(2x-7)(x-5)}{2x-7}
\\\\
h=\dfrac{(\cancel{2x-7})(x-5)}{\cancel{2x-7}}
\\\\
h=x-5
.\end{array}
Hence, the height is $
(x-5) \text{ centimeters}
.$
