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 $12$ inches in $1$ foot, then $1$ $ft$ $2$ $in$ high is equivalent to $14$ $in$ high.

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

\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 $1\text{ }in:4\text{ }ft,$ then the height in the new drawing of the $42$ $ft$ building is

\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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