On an aerial photograph of a triangular piece of land the lengths of the three sides are 4cm, 5cm and 7cm. If the shortest side of the actual piece of land is 360 meters, find the lengths of the other sides
scale is 4cm:360m
so, 5cm = (5/4)4cm : (5/4)360m = 450m
and 7cm = (7/4)4cm : (7/4)360m = 630m
To find the lengths of the other sides of the actual piece of land, we need to scale up the lengths of the sides on the aerial photograph to the actual lengths.
Let's assume the scaling factor is x, where the lengths on the photograph are multiplied by x to get the actual lengths.
The shortest side on the photograph is 4cm. We need to find the value of x that satisfies the equation:
4cm * x = 360m
To solve for x, we need to convert the units.
1 meter = 100 centimeters
360m = 360 * 100cm = 36000cm
Now we can solve for x:
4cm * x = 36000cm
x = 36000cm / 4cm
x = 9000
Therefore, the scaling factor is 9000.
Now, we can find the lengths of the other sides on the actual piece of land:
Shortest side: 4cm * 9000 = 36000cm = 360 meters
Second side: 5cm * 9000 = 45000cm = 450 meters
Longest side: 7cm * 9000 = 63000cm = 630 meters
So, the lengths of the other sides of the actual piece of land are 450 meters and 630 meters.
To find the lengths of the other sides of the actual piece of land, we need to set up a proportion between the lengths of the sides on the aerial photograph and the actual lengths of the sides.
Let's assume the shortest side on the aerial photograph represents the shortest side of the actual piece of land. In this case, we have:
Length of the shortest side on the photograph / Length of the shortest side of the actual land = Length of the other side on the photograph / Length of the other side of the actual land.
Let's plug in the values we know:
4 cm (length of shortest side on photograph) / 360 m (length of the shortest side of actual land) = x cm (length of the other side on the photograph) / y m (length of the other side of actual land).
First, we need to convert all the units to the same type. We can convert either the lengths on the photograph to meters or the lengths of the actual land to centimeters. Let's convert the lengths on the photograph to meters:
4 cm = 0.04 m (Divide by 100, as there are 100 centimeters in a meter).
Now we can plug in the converted values:
0.04 m / 360 m = x cm / y m.
Now let's solve for x. Cross-multiply and solve the equation:
0.04 m * y m = 360 m * x cm.
0.04y = 360x.
To eliminate the units, since we're working with ratios, divide both sides by x:
0.04y / x = 360.
Now we can substitute the given values:
0.04 * (5 cm) / (360 m) = (0.04 * 5) / 360.
0.20 / 360 = x.
Simplifying the expression:
0.00055555 = x.
So, the length of the other side of the actual land is approximately 0.00055555 meters, which is a very small value. This discrepancy is due to a scaling factor when converting from centimeters to meters. However, based on the given information, the exact length cannot be determined without additional information or clarification about the scale of the photograph.