Please Help. NEED HELP WITH GEOMETRY HOMEWORK!

Question

A tower is 40 ft tall and 20 ft wide. A model of the tower is 5 in. Identify the width of the model in inches.

Answer 1

The key to proportion problems is to use appropriate units in the proportions.

For example, if the scale is 1 inches : 1 mile, then how far is 4 inches?

that means:

(1 inch) / (4 miles) = (4 inches) / (x miles)

Now, using cross-multiplication, we see also that:

(4 miles) /1 inch) = (x miles) / (4 inches)

and

(1 inch) / (4 inches) = (4 miles) / (x miles)

and

(4 inches) / (1 inch) = (x miles) / (4 miles)

... just be sure that the units always cancel out.

This problem:

(20 feet wide) / (40 feet tall) = (x inches wide) / (5 inches tall)

[or inverted equation, see examples above]

= (2.5 inches wide) / (5 feet tall)

Get the units right and you won't be converting between inches and feet.

Answer 2

Hi there! I'd love to help you out.

It looks like you're dealing with scales. The original tower is 40 ft tall but the model is 5 in. tall. We can make a proportion to solve this:

height of original tower = height of model

width of original tower width of model

We need to make sure we use the same units in each example as well so we will turn the 40 ft into inches:

1 ft = 12 in.

40 ft * 12 = 480 in for the height

20 ft * 12 = 240 in for the width

Now we can plug it all in and solve our proportion:

480 inches = 5 inches Cross-multiply to solve

240 inches x inches

480x = 1200

/ 480 /480

x = 2.5 inches

So the width of our model is 2.5 inches.

I hope this explanation was thorough and answered all of your questions. If you have additional questions please don't hesitate to reach out! Learn on :)