Question

A building is drawn with a scale of 1 in. : 3 ft. The height of the drawings is 1 ft 2 in. After a design change, the scale is modified to be 1 in : 4 ft. What is the height of the new drawing?

Solution

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Since there are 1212 inches in 11 foot, then 11 ftft 22 inin high is equivalent to 1414 inin high.

Using the scale of 1 in:3 ft,1\text{ }in:3\text{ }ft, then the height of the actual building for a drawing that is 11 ftft 2 inin high is

14 in3 ft1 in=14 in3 ft1 in=14(3) ft=42 ft.\begin{align*} & 14\text{ }in\cdot\dfrac{3\text{ }ft}{1\text{ }in} \\\\&= 14\text{ }\cancel{in}\cdot\dfrac{3\text{ }ft}{1\text{ }\cancel{in}} \\\\&= 14(3)\text{ }ft \\&= 42\text{ }ft .\end{align*}

With the new scale that was changed to 1 in:4 ft,1\text{ }in:4\text{ }ft, then the height in the new drawing of the 4242 ftft building is

42 ft1 in4 ft=42 ft1 in4 ft=424 in=10.5 in.\begin{align*} & 42\text{ }ft\cdot\dfrac{1\text{ }in}{4\text{ }ft} \\\\&= 42\text{ }\cancel{ft}\cdot\dfrac{1\text{ }in}{4\text{ }\cancel{ft}} \\\\&= \dfrac{42}{4}\text{ }in \\\\&= 10.5\text{ }in .\end{align*}

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