Question

A car designer builds models of new designs because, unlike a drawing, a model can be seen from all sides. If you built a 4:5 scale model of a car that is 90ft. long, how long would the full-size prototype be in feet?​

Answer 1

If the scale of the model is 4:5, it means that every linear dimension of the model is 4/5 of the corresponding dimension of the full-size prototype.

Let's call x the length of the full-size prototype in feet.

Then, we can set up the following proportion:

4/5 = model length / full-size prototype length

Solving for the full-size prototype length:

full-size prototype length = model length / (4/5) = model length * (5/4)

The length of the model is 4/5 of the full-size prototype length, so:

model length = (4/5) * x

Substituting this into the equation above:

full-size prototype length = model length * (5/4) = (4/5) * x * (5/4)

Simplifying:

full-size prototype length = x

Therefore, the length of the full-size prototype is:

x = (4/5) * x * (5/4) = 90 feet

So, the full-size prototype would be 112.5 feet long.