Question

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?

Answer 1

Segment drawn on scale having end points O (0,0) and A
`((3)/(4),(9)/(10))` is a line segment.

O A=
`\sqrt{[(3)/(4) -0]^(2) +[(9)/(10) -0]^(2)\\\\`

O A =
`= \sqrt{(9)/(16)+(81)/(100)`

=
`\sqrt(549)/(400)`

=
`(√(549))/(20)`

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

O'B=
`\sqrt{(30-0)^(2)+(36-0)^(2)`

=
`√(900+1296)`

=
`\sqrt {2196}`

= 2√549

`\frac{\text{Actual length}}{\text{Length on scale}}=(OB')/(OA)=(2\sqrt549)/((\sqrt549)/(20))=40` [Cancelling √549 from numerator and denominator]

So, Actual length = 40 × Length on scale