Abigail drew a scale drawing of the oldest house in her town. The actual house is 64 feet long. Abigail's scale drawing is 8 inches long. What scale did Abigail use to draw the house?.

For a particular scale drawing, it is already specified that all the measurements' some constant scaled version will be taken. For example, let the scale be K feet to s inches.

Then it means

[tex]\rm 1\: ft : \dfrac{s}{k}\: in.[/tex]

All feet measurements will then be multiplied by s/k to get the drawing's corresponding lengths.

For this case, we have got:

Actual height of the house = 64 ft

In his scale drawing of the house, the height of the house is 8 inches.

Let the scale he used was K feet to s inches, then:

1 ft: (s/k) inches

64 ft : (s/K) times 64 inches = 8 inches

or

[tex]\dfrac{s}{K} \times 64 = 8\\\text{Dividing both the sides by 64, we get}\\\\\dfrac{s}{K} = \dfrac{1}{8}\\\\[/tex]

comparing them in proportionate way as s and K are only caring about proportion, we get that:

K = 8 feet was converted to s = 1 inches.

Thus, the scale that Abigali used to draw the house was 8 ft : 1 inch

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