Question

A rectangle measures 4 inches by 10 inches. It is dilated using a scale factor of 2.5. What is the area in square inches of the dilated rectangle?(1 point)
Responses

250
250

160
160

2,500
2,500

40
40

Answer 1

To find the area of the dilated rectangle, we first calculate the area of the original rectangle, then apply the scale factor to find the dimensions of the dilated rectangle.

1. **Calculate the area of the original rectangle:**
- Width = 4 inches
- Length = 10 inches
- Area = Width × Length = 4 inches × 10 inches = 40 square inches.

2. **Determine the new dimensions after dilation:**
- New width = Original width × Scale factor = 4 inches × 2.5 = 10 inches
- New length = Original length × Scale factor = 10 inches × 2.5 = 25 inches

3. **Calculate the area of the dilated rectangle:**
- New Area = New Width × New Length = 10 inches × 25 inches = 250 square inches.

Thus, the area of the dilated rectangle is **250 square inches**.