on a map of scale 1:20,000 the area of forest is 50cm^2 .on another map the area of forest is 8cm^2.find the scale of the second map.
i didnt understand
Dimesion of forest on map=2cm ×25cm
Dimesion of actual forest=(2×20000)×(25×20000)
Area of the actual forest=20×10`9 cm2
Scale of the second map=8cm2 : 2×10`10cm2
(By root we get) 1: 50000
Well, let's scale down to the answer, shall we?
If the area of the forest on the first map is 50cm² and the scale is 1:20,000, that means that in reality, the forest occupies 50 cm² * 20,000 = 1,000,000 cm².
Now, if on the second map, the area of the forest is 8cm², we need to find the scale. Let's assume the scale is 1:x.
So, if the area of the forest on the second map is 8cm² and the real area is 1,000,000cm², we can set up a proportion:
1/x = 8/1,000,000
Cross-multiplying, we get:
x = 1,000,000/8
Calculating that, we find:
x = 125,000
Therefore, the scale of the second map is 1:125,000. That's one mighty shrunk-down forest!
To find the scale of the second map, we can set up a proportion between the areas of forest on the two maps.
Let's denote the scale of the second map as "x".
The given information tells us that on the first map with a scale of 1:20,000, the area of the forest is 50 cm².
So, the proportion can be set up as follows:
( Area on Second Map / Area on First Map ) = ( Scale of Second Map / Scale of First Map )
Plugging in the known values:
(8 cm² / 50 cm²) = (x / 20,000)
To find x, we can cross-multiply and solve for x:
8 * 20,000 = 50 * x
160,000 = 50x
Divide both sides of the equation by 50:
x = 160,000 / 50
x = 3,200
Hence, the scale of the second map is 1:3,200.