Question

Nathan is building a model of his father sailboat with a scale factor of 1/32 The actual sale is in the shape of a right triangle with a base of 8 m and a hypotenuse of 13 m what will be the approximate perimeter of the sale on the model boat

Answer 1

Answer:

Perimeter of the model is approximately 1 m.

Step-by-step explanation:

Given:

Scale factor = $\frac{1}{32}$

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,

$h^2=b^2+l^2\\\\13^2=8^2+l^2\\\\l^2=169-64\\\\l=\sqrt{105}=10.25\ m$

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

$\frac{1}{32}=\frac{Model\ perimeter}{31.25}\\\\Model\ perimeter=\frac{31.25}{32}=0.97\approx1\ m$

So, perimeter of the model is approximately 1 m.