A small heater has a rectangular filter that is $13 \text { in. } \times 24 \text { in. }$ Another larger heater requires a similar filter that has a 26 in. width. What is the height of this larger filter?
A) 49 in.
B) 48 in.
C) 27 in.
D) 26 in.
E) 24 in.

Question

Quizplus · Accepted Answer

The filters are similar, so their corresponding sides are proportional. The ratio of the width of the larger filter to the width of the smaller filter is $26 \text{ in.} / 24 \text{ in.} = 13/12$. To find the height of the larger filter, we use the same ratio. The height of the smaller filter is 13 in., so the height of the larger filter is $13 \text{ in.} \times (13/12) = 169/12 \text{ in.} = 14.08 \text{ in.}$. However, none of the options exactly match this calculation, suggesting a mistake in the calculation process. Let's correct it: The correct approach is to maintain the proportion between the sides of the filters. Given the width of the larger filter (26 in.) is twice the width of the smaller filter (13 in.), the height of the larger filter should also be twice the height of the smaller filter, making it $13 \text{ in.} \times 2 = 26 \text{ in.}$, which indicates a mistake in the initial explanation. The correct calculation for the height, based on the proportional relationship, should consider the correct dimensions and ratios, especially noting that the width of the larger filter is given as 26 in., which is not twice but rather a specific ratio compared to the smaller filter's width. The error was in the interpretation of the proportional relationship and the calculation based on that. Given the correct approach to maintain the proportion based on the widths provided (24 in. and 26 in.), the height of the larger filter should be calculated correctly by maintaining the aspect ratio of the original filter.

A Small Heater Has a Rectangular Filter That Is 13 in. ×24 in. 13 \text { in. } \times 24 \text { in. }13 in. ×24 in.

A Small Heater Has a Rectangular Filter That Is $13 \text { in. } \times 24 \text { in. }$