Question

On a scale drawing, $\dfrac{1}{4} = 1 foot$. What are the dimensions on the scale drawings for a room that is $18\ feet$ by $16\ feet$?

Answer 1

Scalar drawings are actual objects or places of two-dimensional representations. Maps and Floor plans are some instances of scale drawings. In the question, the scale on a scale drawing is given. We have to find the dimensions of the room. We have given dimensions in feet. We have to change it in inches.

Complete step-by-step solution:
Given: $\dfrac{1}{4} = 1 foot$
Now, we have to find the dimensions of the room in inches.
The dimensions of room in feet are $18\ feet$ by $16\ feet$.
First, we will convert $18\ feet$ into inches.
$18 feet = 18 \times \dfrac{1}{4} inches$
$\implies 18 feet = \dfrac{9}{2} inches$
$\implies 18 feet = \left( 4 + \dfrac{1}{2} \right) inches$
$\implies 18 feet = 4 \dfrac{1}{2} inches$
First, we will convert $16 feet$ into inches.
$16 feet = 16 \times \dfrac{1}{4} inches$
$\implies 16 feet = \dfrac{16}{2} inches$
$\implies 16 feet = 4 inches$
The dimensions on the scale drawings for a room that is $18 feet$ by $16 feet$ is $4 \dfrac{1}{2}$ inches by $4$ inches.

Note: On a scale drawing, Dimensions on the drawing are expanded or diminished by the equivalent scale sector. Every part resembles something in the actual object. A scale tells us how actual measurements are represented on the drawing.
Sometimes the scale is displayed as a segment on the design itself. A scale drawing is two-dimensional, some features of the three-dimensional objects are not expressed. Scale drawing may not explain every aspect of the actual object; however, the characteristics shown correspond to the real object and follow the particularized scale.