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Answer :
Final answer:
The tree is 45 feet tall. The model plane converts to an actual length of 132 feet. The sketch of the house would have dimensions of 8 cm by 15 cm.
Explanation:
Let's address each scenario:
Tree height:
The tree's shadow is 18 feet.
The building's shadow is 16 feet.
The height of the building is 40 feet.
Using the concept of similar triangles, you can set up a proportion:
Tree Height
Tree Shadow
=
Building Height
Building Shadow
Tree Shadow
Tree Height
=
Building Shadow
Building Height
Plugging in the values:
Tree Height
18
=
40
16
18
Tree Height
=
16
40
Now, solve for the tree height:
Tree Height
=
18
⋅
40
16
=
45
feet
Tree Height=
16
18⋅40
=45 feet
So, the height of the tree is 45 feet (rounded to the nearest foot).
Length of the actual plane:
The model plane's length is 11 inches.
The scale is 1 inch: 12 feet.
To find the actual length of the plane, you can multiply the model's length by the scale factor:
Actual Length
=
Model Length
×
Scale Factor
Actual Length=Model Length×Scale Factor
Actual Length
=
11
×
12
=
132
feet
Actual Length=11×12=132 feet
So, the length of the actual plane is 132 feet (rounded to the nearest foot).
Dimensions of the sketch of the house:
House width: 32 feet
House length: 60 feet
Scale: 1 cm: 4 ft
To find the dimensions of the sketch, you can use the scale factor. For each dimension, divide the actual dimension by the scale factor (4 ft per 1 cm):
Sketch width:
32
ft
4
ft/cm
=
8
cm
4ft/cm
32ft
=8cm
Sketch length:
60
ft
4
ft/cm
=
15
cm
4ft/cm
60ft
=15cm
So, the dimensions of the sketch are:
Width: 8 cm
Length: 15 cm
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