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Question

A parallelogram shows the longer side on the top measuring 9 inches and the shorter side on the right measuring 3 inches.

Tiyane makes a scale drawing of the parallelogram. The longer side of the parallelogram is 22.5 inches in her drawing. What is the length of the parallelogram’s shorter side in Tiyane’s scale drawing?

(1 point)
Responses

7.5 inches
7.5 inches

2.5 inches
2.5 inches

0.4 inches
0.4 inches

60 inches

Answer 1

To find the length of the shorter side in Tiyane's scale drawing, we can set up a proportion based on the original dimensions of the parallelogram and Tiyane's drawing.

The original dimensions are:

• Longer side = 9 inches
• Shorter side = 3 inches

In Tiyane's drawing:

• Longer side = 22.5 inches
• Shorter side = x (unknown)

We can set up a proportion as follows:

\[ \frac{\text{Longer side in drawing}}{\text{Longer side in original}} = \frac{\text{Shorter side in drawing}}{\text{Shorter side in original}} \]

Substituting the known values into the proportion:

\[ \frac{22.5}{9} = \frac{x}{3} \]

Now, we can cross-multiply to solve for x:

\[ 22.5 \cdot 3 = 9 \cdot x \]

Calculating the left side:

\[ 67.5 = 9x \]

Now, divide both sides by 9 to find x:

\[ x = \frac{67.5}{9} = 7.5 \]

Therefore, the length of the parallelogram’s shorter side in Tiyane’s scale drawing is 7.5 inches.