Suppose you dilate a triangle using the scale factor of 1/3. The original side lengths of the triangle measure 11,9 and 28 inches. What is the perimeter of the dilated triangle?

Question

perimeter = _ in

Answer 1

To find the perimeter of the dilated triangle, we first need to calculate the new side lengths after applying the dilation scale factor of \( \frac{1}{3} \).

The original side lengths of the triangle are:

• Side 1: 11 inches
• Side 2: 9 inches
• Side 3: 28 inches

Now, we will multiply each side length by the scale factor:

1. New Side 1: \[ 11 \times \frac{1}{3} = \frac{11}{3} \text{ inches} \]

2. New Side 2: \[ 9 \times \frac{1}{3} = 3 \text{ inches} \]

3. New Side 3: \[ 28 \times \frac{1}{3} = \frac{28}{3} \text{ inches} \]

Next, we calculate the perimeter of the dilated triangle by adding the new side lengths:

\[ \text{Perimeter} = \frac{11}{3} + 3 + \frac{28}{3} \]

To add these, we first express 3 as a fraction with a common denominator of 3:

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

Now we can add the fractions: \[ \text{Perimeter} = \frac{11}{3} + \frac{9}{3} + \frac{28}{3} \] \[ \text{Perimeter} = \frac{11 + 9 + 28}{3} = \frac{48}{3} = 16 \text{ inches} \]

Therefore, the perimeter of the dilated triangle is: \[ \text{perimeter} = 16 \text{ in} \]