Picky Rectangles

A \(150\times 70\) grid has \(178\ x\times y\) rectangles. Find the value of \(x+y\).

Details and Assumptions:

  • Dimensions are expressed as width\(\times\)height. Thus an \(x\times y\) rectangle (that is, a rectangle of width \(x\) and height \(y\)) is considered to be different from a \(y\times x\) (width \(y,\) height \(x\)) rectangle. In this problem, you only consider the \(x\times y\) rectangles, not the \(y\times x\) ones.

This is one part of Quadrilatorics.
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