Respuesta :
Answer:
Perimeter of the model is approximately 1 m.
Step-by-step explanation:
Given:
Scale factor = [tex]\frac{1}{32}[/tex]
Actual base length of the sailboat (b) = 8 m
Actual hypotenuse length of the sailboat (h) = 13 m
Using Pythagoras theorem, we can find the third side of the right angled sailboat. Let the third side be 'l' m. So,
[tex]h^2=b^2+l^2\\\\13^2=8^2+l^2\\\\l^2=169-64\\\\l=\sqrt{105}=10.25\ m[/tex]
Now, actual perimeter of the sailboat = Sum of all the 3 sides
Actual perimeter = 13 m + 8 m + 10.25 m = 31.25 m
Now, we know that,
Scale factor = Model dimensions ÷ Actual dimensions
So, in terms of perimeter,
Scale factor = Model perimeter ÷ Actual perimeter
[tex]\frac{1}{32}=\frac{Model\ perimeter}{31.25}\\\\Model\ perimeter=\frac{31.25}{32}=0.97\approx1\ m[/tex]
So, perimeter of the model is approximately 1 m.
