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)

Question

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.