Drawing 2 is 3/8 the size of Drawing 1, and Drawing 3 is twice the size of Drawing 2. Find the scale factor from Drawing 1 to Drawing 3.

Question

 Scale factor between 2 drawings.

Answer 1

Note that scale factors for drawings are linear (that is, inches, not square inches).

 

It's usually O.K. to use the numbers in the ratios to check the relative sizes.  So,

  If "Drawing 2 is 3/8 the size of Drawing 1"    that means

            D2 = 3

            D1 = 8

  If "Drawing 3 is twice the size of Drawing 2"   that means

            D3 = 2*D2

            D3= 6

  Now, "Find the scale factor from Drawing 1 to Drawing 3"

            D1=8 and D3=6    so the ratio is  8:6

     We usually reduce this to the smallest integers -- 

          So, the scale factor from D1 to D3 is 4 to 3.  "Drawing 1 is 1 1/3 times the size of Drawing 3."

 

Answer 2

Drawing 2 (D₂) is 3/8 times the size of Drawing 1 (D₁).

Drawing 3 (D₃) is 2 times the size of D₂.

Therefore the scale factor from D₁ to D₃ is 3/8 * 2 or 6/8 which simplifies to 3/4.

 

Check: 

        if D₁ = 8, then D₂ = 3/8 * 8 = 3.  This would make D₃ = 2 * 3 = 6.

        D₁ * 3/4 = 8 * 3/4 = 6.