Question

A rectangular parking lot is 120 feet long and 75 feet wide. Diego made another scale drawing of the parking lot at a scale of 1 to 180. The drawing he produced is also 8 inches by 5 inches. (Remember the video. Scales with no units represent the SAME UNIT. So how is Diego using a different scale than Lin, but ended up with the same drawing?) (12 inches = 1 foot) 2.) Explain or show how Diego's scale would produce an 8 inch by 5-inch drawing.

Answer 1

Answer:

We kindly invite you to read carefully the explanation detailed below for further details.

Step-by-step explanation:

At first we understand that Diego converted length and wide units from feet to inches ($1\,ft = 12\,in$) and then he divided each term by 180, since he was using a reduction scale, so that rectangular parking lot can be represented on paper. That is:

Step 1 - Unit conversion:

$l = 120\,ft$ ($l$ - Length)

$l = 120\,ft\times \frac{12\,in}{1\,ft}$

$l = 1440\,in$

$w = 75\,ft$ ($w$ - Width)

$w = 75\,ft\times \frac{12\,in}{1\,ft}$

$w = 900\,in$

Step 2 - Applying scaling:

$l' = \frac{l}{180}$ ($l'$ - Scaled length)

$l' = \frac{1440\,in}{180}$

$l' = 8\,in$

$w' = \frac{w}{180}$ ($w'$ - Scaled width)

$w' = \frac{900\,in}{180}$

$w' = 5\,in$