Math  /  Geometry

Question(2.) A polygon has perimeter 12 units. It is dilated with a scale factor of 34\frac{3}{4}. What is the perimeter of its image? A. 9 units B. 12 units C. 16 units D. It cannot be determined. (3.) Triangle ABCA B C is taken to triangle ABCA^{\prime} B^{\prime} C^{\prime} by a dilation. Which of these scale factor for the dilation would result in an image that was larger than the original figure? A. 35\frac{3}{5} B. 1317\frac{13}{17} C. 1 D. 43\frac{4}{3}

Studdy Solution

STEP 1

1. For problem (2), the dilation of a polygon affects its perimeter by the same scale factor.
2. For problem (3), a scale factor greater than 1 will result in an image larger than the original figure.

STEP 2

1. Solve problem (2) by applying the scale factor to the perimeter.
2. Solve problem (3) by analyzing the scale factors.

STEP 3

For problem (2), we start with the original perimeter of the polygon, which is 12 units. The polygon is dilated with a scale factor of 34 \frac{3}{4} .

STEP 4

To find the perimeter of the dilated image, multiply the original perimeter by the scale factor:
Perimeter of image=Original perimeter×Scale factor \text{Perimeter of image} = \text{Original perimeter} \times \text{Scale factor} =12×34 = 12 \times \frac{3}{4}

STEP 5

Calculate the result:
12×34=12×0.75=9 12 \times \frac{3}{4} = 12 \times 0.75 = 9
The perimeter of the image is 9 units, which corresponds to option A.

STEP 6

For problem (3), we need to determine which scale factor results in an image larger than the original triangle. A scale factor greater than 1 will enlarge the figure.

STEP 7

Evaluate each option: - A. 35=0.6 \frac{3}{5} = 0.6 , which is less than 1. - B. 13170.7647 \frac{13}{17} \approx 0.7647 , which is less than 1. - C. 1, which results in the same size. - D. 431.3333 \frac{4}{3} \approx 1.3333 , which is greater than 1.
The scale factor that results in an image larger than the original figure is 43 \frac{4}{3} , which corresponds to option D.

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