Certainly! Let's solve this step by step.
We have a rectangle with an initial width of 2 inches and an initial height of 3 inches. The height of the rectangle is enlarged to 18 inches. We need to determine the new width of the rectangle.
First, let's calculate the scale factor by comparing the new height to the initial height:
[tex]\[ \text{Scale factor} = \frac{\text{New height}}{\text{Initial height}} \][/tex]
Given:
[tex]\[ \text{Initial height} = 3 \text{ inches} \][/tex]
[tex]\[ \text{New height} = 18 \text{ inches} \][/tex]
So,
[tex]\[ \text{Scale factor} = \frac{18}{3} = 6 \][/tex]
Next, we use the scale factor to find the new width by multiplying the initial width by this scale factor:
[tex]\[ \text{Initial width} = 2 \text{ inches} \][/tex]
[tex]\[ \text{New width} = \text{Initial width} \times \text{Scale factor} \][/tex]
Thus,
[tex]\[ \text{New width} = 2 \times 6 = 12 \text{ inches} \][/tex]
Therefore, the new width of the rectangle is 12 inches. The correct choice is:
(B) 12 in
