On a map, 1 centimeter represents 7½cm kilometers. What length On the map would represent a distance of 45 kilometers?
To find the length on the map that represents a distance of 45 kilometers, we need to use the given scale of 1 centimeter representing 7½ kilometers.
First, we need to determine how many centimeters equal 1 kilometer:
1 centimeter represents 7½ kilometers
Therefore, 1 kilometer represents 1/(7½) = 2/15 centimeters.
Next, we can calculate the length on the map that represents 45 kilometers:
45 kilometers represents (45 * 2/15) = 6 centimeters.
Therefore, a length of 6 centimeters on the map would represent a distance of 45 kilometers.
To determine the length on the map that represents a distance of 45 kilometers, we need to use the given scale. The scale states that 1 centimeter on the map represents 7½ kilometers.
We can set up a proportion to solve for the unknown length on the map:
1 cm / 7½ km = x cm / 45 km
To solve for x, we can cross-multiply:
7½ km * x cm = 1 cm * 45 km
We can simplify:
7½x = 45
Now, divide both sides by 7½:
x = 45 / 7½
To simplify further, we can convert 7½ to an improper fraction:
7½ = 7 + ½ = 15/2
Now, substitute 15/2 for 7½:
x = 45 / (15/2)
To divide by a fraction, we multiply by its reciprocal:
x = 45 * (2/15)
Simplifying the multiplication:
x = 6 cm
Therefore, a length of 6 centimeters on the map would represent a distance of 45 kilometers.
To find out the length on the map that represents a distance of 45 kilometers, we need to use the scale given in the question. The scale on the map states that 1 centimeter represents 7½ kilometers.
First, we determine the ratio between the distance on the map and the actual distance:
1 centimeter represents 7½ kilometers.
To simplify the calculation, let's convert 7½ kilometers into a decimal:
7½ kilometers = 7.5 kilometers.
Now we have:
1 centimeter represents 7.5 kilometers.
Next, we need to find the length on the map that represents 45 kilometers. We can set up a proportion to solve for this value:
1 centimeter is to 7.5 kilometers as X centimeters is to 45 kilometers.
Using cross-multiplication, we get:
1 * 45 = 7.5 * X.
Simplifying this equation, we find:
45 = 7.5X.
To solve for X, we divide both sides of the equation by 7.5:
X = 45 / 7.5.
Evaluating this equation, we get:
X = 6.
Therefore, on the map, a length of 6 centimeters would represent a distance of 45 kilometers.