Question

Michael is making scale drawings of rectangular rooms using a scale of 1 inch : 1 and 1/2 feet. He wants to use paper that has a width of 8 and 1/2 inch and a length of 11 in for the drawing. Determine whether the scale drawings for each of these rooms will fit on one piece of paper.

Choose yes or no for each set of dimensions:

16 feet by 16 feet: yes or no?

10 ft by 15 ft: yes or no?

15 ft by 20 ft: yes or no

12 ft by 16 ft: yes or no?

Answer 1

16ft by 16 ft: NO

10ft by 15ft: YES

15ft by 20ft: NO

12ft by 16ft: YES

Explanation:

First, we know that the scale used is:

1 in = (1 + 1/2) ft.

This means that each inch on the drawing is equivalent to (1 + 1/2) ft.

We know that Michael uses a paper that has the measures:

width = (8 + 1/2) in

length = 11in

Then the maximum dimensions that can be represented with this paper are:

WIDTH = (8 + 1/2)*(1 + 1/2) ft. = (8 + 8/2 + 1/2 + 1/4) ft

= (8 + 4 + 2/4 + 1/4) ft

= (12 + 3/4) ft

LENGTH = 11*(1 + 1/2) ft = (11 + 11/2)ft = (11 + 10/2 + 1/2)ft

= (11 + 5 + 1/2)ft = (16 + 1/2) ft.

Now let's analyze the options, we can only draw the rooms in the paper if the measures are equal or smaller than the ones we found above:

Where the measures are written as: "width by length".

a) 16ft by 16 ft.

width = 16ft

length = 16ft

We can not draw this, because the maximum width that we can draw is (12 + 3/4) ft, which is smaller than 16ft.

b) 10 ft by 15 ft

width = 10ft

length = 15ft

Both are smaller than the maximum measures we found, then yes, we can draw this room.

c) 15 ft by 20 ft

width = 15ft

length = 20ft

Both are larger than the maximum measures, so no, we can not draw this.

d) 12ft by 16ft

width = 12ft < (12 + 3/4) ft = maximum width

lenth = 16ft < (16 + 1/2) ft = maximum length.

Both measures are smaller than the maximum ones, then we can draw this one