Use the table to answer the question.

Original Poster Scale Drawing
left edge (in.) 36 ?
top edge (in.) 24 8
A local food organization puts out a healthy foods poster. The poster is in the shape of a rectangle, and its dimensions are given in the table. Alfredo wants to make a smaller version of the poster to hang up in the community center. He makes a scale drawing of the poster with the length of the top edge given in the table. What is the area of Alfredo’s scale drawing?

(1 point)
Responses

1/3
square meters
Start Fraction 1 over 3 end fraction square meters

12 square inches
12 square inches

96 square inches
96 square inches

192 square inches

1 answer

To find the area of Alfredo's scale drawing, we first need to determine the scale factor used for the top edge of the original poster compared to the scaled drawing.

The original dimensions of the poster are:

  • Left edge: 36 inches
  • Top edge: 24 inches

The scale drawing has the top edge as 8 inches. We can calculate the scale factor by comparing the scaled top edge to the original top edge:

\[ \text{Scale factor} = \frac{\text{Scaled top edge}}{\text{Original top edge}} = \frac{8 , \text{inches}}{24 , \text{inches}} = \frac{1}{3} \]

Next, we apply this scale factor to find the scaled left edge. Since the left edge of the original poster measures 36 inches:

\[ \text{Scaled left edge} = \text{Original left edge} \times \text{Scale factor} = 36 , \text{inches} \times \frac{1}{3} = 12 , \text{inches} \]

Now, we can calculate the area of the scale drawing. The area \(A\) of a rectangle is given by the formula:

\[ A = \text{width} \times \text{height} \]

For the scale drawing, we have:

  • Height (top edge) = 8 inches
  • Width (left edge) = 12 inches

Now, calculate the area:

\[ A = 12 , \text{inches} \times 8 , \text{inches} = 96 , \text{square inches} \]

Thus, the area of Alfredo's scale drawing is 96 square inches.

The correct response is:

96 square inches.