Proportions & Scale Factors Practice
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4 of 54 of 5 Items
Question
Use the image to answer the question.
A grid is shown with a rectangle drawn on it. The rectangle is 3 units long and 2 units wide, labeled with 3 and 2 respectively.
Scale: 1 box = 15 feet
Convert this scale drawing so that it has a scale of 1 box = 5 feet. The width in the scale drawing shown is 2 boxes. What will be the width in boxes of the new scale drawing?
(1 point)
To answer this question, we need to understand the concept of scale factor. The scale factor is the ratio of the lengths of two corresponding sides in two similar geometric figures.
Given the original scale of 1 box = 15 feet, we can determine the length of each box in the grid. Since the length of the rectangle is 3 units, we can calculate the actual length using the scale factor.
Original length of rectangle = 3 units
Scale factor = 1 box / 15 feet
Actual length of rectangle = Scale factor * Original length of rectangle
= (1 box / 15 feet) * 3 units
= 3/15 feet
= 1/5 feet
Now, let's calculate the width of the rectangle in the scale drawing shown. It is given that the width is 2 boxes. We can use the scale factor to convert it to the actual width.
Width in actual scale = Scale factor * Width in scale drawing
= (1/5 feet/box) * 2 boxes
= 2/5 feet
Now, we are asked to convert the scale drawing to a new scale of 1 box = 5 feet. This means we need to determine how many boxes will represent the width in the new scale.
Width in new scale = Width in actual scale / Scale factor of new scale
= (2/5 feet) / (5 feet/box)
= 2/25 feet per box
Therefore, the width in boxes of the new scale drawing will be 2/25 boxes.
wrong
The ratio of the original scale to the new scale is 15 feet : 5 feet, which simplifies to 3 : 1.
Since the width in the original scale drawing is 2 boxes, we can find the width in the new scale drawing by dividing 2 by the ratio 3:1.
2 / 3 = 0.67
Therefore, the width in the new scale drawing will be approximately 0.67 boxes.
Apologies for the incorrect answer. Let's try to solve the question again.
The original scale is 1 box = 15 feet. In the new scale, 1 box is equal to 5 feet.
To find the width in the new scale drawing, we need to find the ratio between the new scale and the original scale.
New scale width = (Original scale width) * (New scale ratio / Original scale ratio)
The original scale width is 2 boxes, and the original scale ratio is 15 feet : 1 box. The new scale ratio is 5 feet : 1 box.
New scale width = 2 * (5/15)
Simplifying the expression, we get:
New scale width = 2 * (1/3)
New scale width = 2/3
Therefore, the width in the new scale drawing will be 2/3 of a box.