On a map,1centimeter represents 7 1/2cm kilometers.what length 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 can set up a proportion.
Let's represent the length on the map as x centimeters.
According to the given information, 1 centimeter on the map represents 7 1/2 kilometers.
Thus, our proportion is:
1 cm / 7 1/2 km = x cm / 45 km
To solve for x, we can cross-multiply and then divide:
1 * 45 km = 7 1/2 km * x cm
45 km = 15/2 km * x cm
Next, let's simplify the right side by finding a common denominator:
45 km = 15/2 * 2/2 km * x cm
45 km = 30/2 km * x cm
45 km = 15 km * x cm
Now, we can isolate x by dividing both sides by 15 km:
45 km / 15 km = x cm
3 = x cm
Therefore, on the map, a distance of 45 kilometers would be represented by a length of 3 centimeters.
To find the length on the map that represents a distance of 45 kilometers, we can use the given scale: 1 centimeter represents 7 1/2 kilometers.
First, we calculate the length on the map for 1 kilometer:
Length on map for 1 kilometer = 1 centimeter × (1 kilometer / 7 1/2 kilometers)
= 1 centimeter / (15/2)
= 1 centimeter × (2/15)
= 2/15 centimeters
Next, we calculate the length on the map for 45 kilometers:
Length on map for 45 kilometers = 45 kilometers × (2/15 centimeters / 1 kilometer)
= 45 kilometers × (2/15 centimeters)
= (45 × 2) / 15 centimeters
= 90 / 15 centimeters
= 6 centimeters
Therefore, a length of 6 centimeters on the map would represent a distance of 45 kilometers.