Suppose an architect draws a segment on a scale drawing with the end points (0,0) and (3⁄4,9⁄10). the same segment on the actual structure has the end points (0,0) and (30,36). what proportion could model this situation?

Segment drawn on scale having end points O (0,0) and A is a line segment.

O A=

O A =

     =

    =

Now ,  the same segment actual structure having end points O'(0,0) and B (30,36) is also a line segment.

O'B=

     =

     =

     = 2√549

[Cancelling √549 from numerator and denominator]

So, Actual length = 40 × Length on scale

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x = 3 ± √(5+y)