I need help with proportions...?

Question

so yea this is the question...

1. On a map showing the mythical land of Nordor, 1.2cm represents 24 km. It is approximately 5cm from Knight Rock to Storm Bay on the map. What is the actual distance is kilometers?

2. A 6-ft fence casts a shadow of 15 ft. At the same time, a tree casts a shadow of 22 ft. How tall is the tree?

3. On a map, 1 in. represents 360 mi. Tow cities are 3/4 in. apart on the map. How far apart are the two cities?

Answer 1

Hi,

1. On a map showing the mythical land of Nordor, 1.2cm represents 24 km. It is approximately 5cm from Knight Rock to Storm Bay on the map. What is the actual distance is kilometers?

1.2........5
-----..=..---
24.........x

This is map over actual equals map over actual.
Now cross multiply.

1.2x = 5(24)
1.2x = 120
x = 100 km

2. A 6-ft fence casts a shadow of 15 ft. At the same time, a tree casts a shadow of 22 ft. How tall is the tree?

This is object over shadow equals object over shadow.

6.........x
----.=.-----
15......22

Now cross multiply.

15x = 6(22)
15x = 132
x = 44/5 or 8 4/5 ft is the height of the tree.

3. On a map, 1 in. represents 360 mi. Tow cities are 3/4 in. apart on the map. How far apart are the two cities?

map over kiles = map/miles

..1........3/4
------.=.------
360.......x

x = 3/4(360)
x = 270 miles


I hope that helps!! :-)

Answer 2

1) Let the actual distance be x kilometers
Therefore x/5=24/1.2
or,x=24*5/1.2
=100
Therefore,the actual distance is 100 km
2)Let the tree be x feet tall
Therefore x/22=6/15
or,15x=22*6 [by cross-multiplication]
or, x=22*6/15=8.8
Therefore,the tree is 8.8 ft long
3.let the actual distnce between the two cities be x miles
Therefore, 1/360=(3/4)/x
or,x=3*360/4=270
Hence the actual distance is 270 miles

Answer 3

1. 1.2 cm = 24 km, so 1.2/24 =5/x
So x = 100 km

2. 6/15 = x/22
So tree = 8.8 feet

3. 1=360 so 1/360 = .75/x
So cities are 270 mi. apart

Answer 4

1.
1.2/24 = 5/x
1.2x = 5*24
1.2x = 120
x = 100km

2.
6/15 = x/22
6*22 = 15x
15x = 132
x = 8.8 ft tall

3.
1/360 = 0.75/x
x = 0.75*360
x = 270 mi