Question

An interior decorator creates a scale drawing of the conference room. If the longer side of the scale drawing is 4 in., what is the area of the scale drawing

a-120 in 2
b-44 in 2
c-14 in 2
d-12 in 2

Answer 1

The dimensions of the scale drawing are 1.5 cm by 2.5 cm. Using the proportion, we can find the actual dimensions and then calculate the area of the scale drawing.

Step-by-step explanation:

To find the area of the scale drawing, we need to know the dimensions of the actual conference room. Since the scale factor is 1 centimeter-2 meters, we can set up a proportion to find the dimensions of the actual room. The dimensions of the scale drawing are 1.5 centimeters by 2.5 centimeters. We can set up the proportion: (scale length)/(actual length) = (scale width)/(actual width). Plugging in the values, we get: (1.5 cm)/(actual length) = (2.5 cm)/(actual width). Rearranging the equation, we have: (1.5 cm)(actual width) = (2.5 cm)(actual length). Solving for the actual width, we get: actual width = (2.5 cm)(actual length)/(1.5 cm).

Now, we can find the area of the scale drawing by multiplying the length and width: area = (1.5 cm)(2.5 cm) = 3.75 cm². Therefore, the area of the scale drawing is 3.75 cm².