To find the new dilated perimeter of rectangle LMNO after applying a scale factor of 1.5, we first need to calculate the original perimeter of the rectangle.
The perimeter (P) of a rectangle is given by the formula:
\[ P = 2 \times (\text{length} + \text{width}) \]
In this case, the length is 16 units and the width is 9.5 units. Therefore, the original perimeter is:
\[ P = 2 \times (16 + 9.5) \]
Now, when we dilate the rectangle using a scale factor of 1.5, the new perimeter can be calculated by applying the scale factor to the original perimeter:
\[ \text{New Perimeter} = 1.5 \times P = 1.5 \times (2 \times (16 + 9.5)) \]
Now, let's look at the response options provided:
- 1.5(16 + 9.5)
- 1.5(2⋅16) + 1.5(2⋅9.5)
- 1.5(16) + 1.5(9.5)
- 1.5(2⋅16 + 9.5)
The correct expression should resemble the equation we derived for the new perimeter, which incorporates both the scale factor and the total original perimeter, i.e., \(1.5 \times 2 \times (16 + 9.5)\).
Among the options:
- The first option does not multiply by 2, so it is incorrect.
- The second option can be derived and looks valid: \(1.5(2 \cdot 16) + 1.5(2 \cdot 9.5) = 1.5 \times 2 \times (16 + 9.5)\).
- The third option does not correctly account for the perimeter’s full calculation since it ignores the multiplication by 2.
- The fourth option incorrectly combines the addition of 9.5 instead of the proper perimeter calculation.
Thus, the correct expression for the new dilated perimeter is:
1.5(2⋅16) + 1.5(2⋅9.5)
1 answer