An illustration shows two triangles positioned differently. The first triangle has its longest side along the baseline. The second triangle has its longest side in the upper left, and the triangle is tilted upward to the right. The first triangle has a base of 18 inches and sides as 10 inches and 15 inches. The second triangle shows three sides as 30 inches, 36 inches, and 20 inches.

Question

Randee draws these two triangles with lengths given in centimeters. What scale factor does she use to create the copy on the right from the original on the left?

(1 point)
Responses

1/2
Start Fraction 1 over 2 End Fraction

1 1/3
1 Start Fraction 1 over 3 End Fraction

2
2

1 2/3

Answer 1

To find the scale factor Randee uses to create the second triangle from the first, we need to convert the given dimensions of both triangles into the same units. Since the lengths in the question are given in inches and Randee is drawing them in centimeters, we will just work with the ratios of the corresponding sides regardless of the unit.

1. First triangle dimensions:

   • Base: 18 inches
   • Other sides: 10 inches, 15 inches

2. Second triangle dimensions:

   • Sides: 30 inches, 36 inches, 20 inches

Now, we will compare the sides of the triangles to find the scale factor.

Let's choose a side from the first triangle to compare with a corresponding side from the second triangle:

For the longest side:

• First Triangle: 18 inches
• Second Triangle: 36 inches

Now, let's calculate the scale factor: \[ \text{Scale Factor} = \frac{\text{Side of the second triangle}}{\text{Side of the first triangle}} = \frac{36}{18} = 2 \]

Now, let's check with the other sides to ensure consistency:

• Compare 10 inches (first triangle) with a side from the second triangle: Using the 20 inches side, \[ \text{Scale Factor} = \frac{20}{10} = 2 \]

• Compare 15 inches (first triangle) with a side from the second triangle: Using the 30 inches side, \[ \text{Scale Factor} = \frac{30}{15} = 2 \]

Since the scale factor is consistently 2 for all corresponding sides, the scale factor Randee uses to create the copy on the right from the original on the left is:

2.

Answer 2

A grid is shown with a rectangle drawn on it. The rectangle is 6 units long and 2 units wide, labeled with 6 and 2 respectively. Scale: 1 box = 4 centimeters Reproduce the scale drawing so that it has a scale of 1 box = 2 centimeters. Which shows the correct new scale drawing? (1 point) Responses A grid is shown with a rectangle drawn on it. The rectangle is 3 units long and 1 unit wide, labeled with 3 and 1 respectively. Scale: 1 box = 2 centimeters Image with alt text: A grid is shown with a rectangle drawn on it. The rectangle is 3 units long and 1 unit wide, labeled with 3 and 1 respectively. Scale: 1 box = 2 centimeters A grid is shown with a rectangle drawn on it. The rectangle is 12 units long and 4 units wide, labeled with 12 and 4 respectively. Scale: 1 box = 2 centimeters Image with alt text: A grid is shown with a rectangle drawn on it. The rectangle is 12 units long and 4 units wide, labeled with 12 and 4 respectively. Scale: 1 box = 2 centimeters A grid is shown with a rectangle drawn on it. The rectangle is 6 units long and 3 units wide, labeled with 6 and 3 respectively. Scale: 1 box = 2 centimeters Image with alt text: A grid is shown with a rectangle drawn on it. The rectangle is 6 units long and 3 units wide, labeled with 6 and 3 respectively. Scale: 1 box = 2 centimeters A grid is shown with a rectangle drawn on it. The rectangle is 12 units long and 2 units wide, labeled with 12 and 2 respectively. Scale: 1 box = 2 centimeters

Answer 3

To reproduce the original rectangle (6 units long and 2 units wide) at a new scale of 1 box = 2 centimeters, we first need to calculate the dimensions of the rectangle in terms of the new scale.

Original Dimensions

• Length: 6 units
• Width: 2 units

Convert these dimensions to the new scale (1 box = 2 centimeters):

• Length in centimeters: \(6 \text{ units} \times 2 \text{ cm/unit} = 12 \text{ cm}\)
• Width in centimeters: \(2 \text{ units} \times 2 \text{ cm/unit} = 4 \text{ cm}\)

New Dimensions in the new scale:

• Length: 12 cm
• Width: 4 cm

Corresponding Unit Representation in the New Scale Drawing

Now, if we represent these dimensions in the new grid:

• Length (12 cm) translates back into the unit count using 1 box = 2 cm: \[ \text{Length in units} = \frac{12 \text{ cm}}{2 \text{ cm/unit}} = 6 \text{ units} \]
• Width (4 cm) translates back into the unit count using 1 box = 2 cm: \[ \text{Width in units} = \frac{4 \text{ cm}}{2 \text{ cm/unit}} = 2 \text{ units} \]

Now we look for the correct representation among the responses:

1. Rectangle with 3 units long and 1 unit wide. (3 units and 1 unit)
2. Rectangle with 12 units long and 4 units wide. (12 units and 4 units)
3. Rectangle with 6 units long and 3 units wide. (6 units and 3 units)
4. Rectangle with 12 units long and 2 units wide. (12 units and 2 units)

Since we calculated that the correct dimensions should be 12 units by 4 units:

The correct new scale drawing is the one that shows the rectangle as 12 units long and 4 units wide.