You are reducing a map of dimensions 2ft by 3ft to fit to a piece of paper 8in by 10in. What are the dimensions of the largest possible map that can fit on the page?
To determine the dimensions of the largest possible map that can fit on the page, we need to find the scale factor or the ratio of the dimensions of the original map to the dimensions of the paper.
Let's first convert the dimensions of the original map to inches:
Original map dimensions: 2ft by 3ft
1 ft = 12 inches
So, the original map dimensions in inches are:
Width: 2ft * 12in/ft = 24in
Height: 3ft * 12in/ft = 36in
Now, let's find the scale factor:
Scale factor = (Dimensions of the paper) / (Dimensions of the original map)
Width scale factor = 8in / 24in = 1/3
Height scale factor = 10in / 36in = 5/18
Since we want to reduce the map to fit on the page, we need to find the minimum scale factor. In this case, the minimum scale factor is 1/3.
To find the dimensions of the largest possible map that can fit on the page, we multiply the dimensions of the original map by the scale factor:
Width of the largest possible map = Width of the original map * Scale factor
Width of the largest possible map = 24in * (1/3) = 8in
Height of the largest possible map = Height of the original map * Scale factor
Height of the largest possible map = 36in * (1/3) = 12in
Therefore, the dimensions of the largest possible map that can fit on the page are 8in by 12in.
To find the dimensions of the largest possible map that can fit on the page, we first need to convert all the measurements to the same units (either inches or feet). Let's convert the dimensions of the original map from feet to inches.
Given:
Dimensions of the original map: 2 ft x 3 ft
Dimensions of the paper: 8 in x 10 in
1 foot = 12 inches
So, the dimensions of the original map in inches are:
2 ft x 12 in/ft = 24 in x 3 ft x 12 in/ft = 36 in
Now, let's compare the dimensions of the original map with the dimensions of the paper and determine which dimension will be the limiting factor.
For the length:
Original map length = 36 in
Paper length = 10 in
Since 36 in is greater than 10 in, the length of the original map will be the limiting factor.
For the width:
Original map width = 24 in
Paper width = 8 in
Since 24 in is greater than 8 in, the width of the original map will be the limiting factor.
To find the largest possible map that can fit on the page, we must consider both the length and the width.
From the calculations above, we determined that the length of the original map is the limiting factor, so we'll use the paper length as the limit. Therefore, the maximum length of the map that can fit on the page is 10 inches.
Similarly, the width of the original map is the limiting factor, so we'll use the paper width as the limit. Therefore, the maximum width of the map that can fit on the page is 8 inches.
Hence, the dimensions of the largest possible map that can fit on the paper are 8 inches by 10 inches.