Question

A) A trapezoid has a base of 10 inches, sides of 8 inches, and a top length of 4 inches. Suppose
the trapezoid is dilated using a scale factor of
1
2
. What is the perimeter of the dilated trapezoid?
(1 point)
11 inches
15 inches
30 inches
60 inches
A) Ross draws a triangle with side lengths of 6, 6, and 5 cm. Suppose he plans to draw the same
triangle dilated with a scale factor of 4. What is the perimeter of the dilated triangle? (1 point)
68 cm
17 cm
34 cm
8.5 cm

Answer 1

To find the perimeter of a dilated trapezoid and triangle, we'll follow these steps:

### Part A: Trapezoid

1. **Calculate the original perimeter of the trapezoid**:
- Base = 10 inches
- Side 1 = 8 inches
- Side 2 = 8 inches (since the trapezoid has two equal sides)
- Top length = 4 inches

\[
\text{Perimeter} = \text{Base} + \text{Side 1} + \text{Side 2} + \text{Top} = 10 + 8 + 8 + 4 = 30 \text{ inches}
\]

2. **Dilate the trapezoid with a scale factor of \( \frac{1}{2} \)**:
- A scale factor of \( \frac{1}{2} \) means that the new perimeter will also be multiplied by \( \frac{1}{2} \).

\[
\text{Dilated Perimeter} = \text{Original Perimeter} \times \frac{1}{2} = 30 \times \frac{1}{2} = 15 \text{ inches}
\]

### Answer for Part A: 15 inches

---

### Part B: Triangle

1. **Calculate the original perimeter of the triangle**:
- Side 1 = 6 cm
- Side 2 = 6 cm
- Side 3 = 5 cm

\[
\text{Perimeter} = \text{Side 1} + \text{Side 2} + \text{Side 3} = 6 + 6 + 5 = 17 \text{ cm}
\]

2. **Dilate the triangle with a scale factor of 4**:
- A scale factor of 4 means that the new perimeter will be multiplied by 4.

\[
\text{Dilated Perimeter} = \text{Original Perimeter} \times 4 = 17 \times 4 = 68 \text{ cm}
\]

### Answer for Part B: 68 cm

---

**Final Answers:**
- Part A: 15 inches
- Part B: 68 cm