Math  /  Geometry

Question2. Gregory draws a scale drawing of a rectangular room The scale that he uses is 1 cm:4ft1 \mathrm{~cm}: 4 \mathrm{ft}. On the drawing, tt room is 3 centimeters long. Which equation can be uu to find the actual length of the room? A 14=x3\frac{1}{4}=\frac{x}{3} C 14=3x\frac{1}{4}=\frac{3}{x} B x4=13\frac{x}{4}=\frac{1}{3} D 1x=43\frac{1}{x}=\frac{4}{3} Rob chose A\mathbf{A} as the correct answer. How did he get that answer?

Studdy Solution

STEP 1

What is this asking? We need to find the real length of a room given a scale drawing where 1 cm represents 4 ft and the drawing shows the room as 3 cm long. Watch out! Don't mix up the units, and make sure your equation correctly relates the scale to the real length.

STEP 2

1. Set up the proportion
2. Analyze Rob's mistake

STEP 3

The scale is 1 cm : 4 ft\text{1 cm : 4 ft}, meaning that every 1 cm\text{1 cm} on the drawing equals 4 ft\text{4 ft} in real life.
This is super important!

STEP 4

We can write this scale as a fraction: 1 cm4 ft\frac{1 \text{ cm}}{4 \text{ ft}}.
This fraction is our **key** to unlocking the real length!

STEP 5

Let's call the actual length of the room xx ft\text{ft}.
We want to find the value of xx.

STEP 6

We can write another fraction representing the relationship between the drawing length and the real length: 3 cmx ft\frac{3 \text{ cm}}{x \text{ ft}}.

STEP 7

Now, we set these two fractions equal to each other to create a proportion: 1 cm4 ft=3 cmx ft\frac{1 \text{ cm}}{4 \text{ ft}} = \frac{3 \text{ cm}}{x \text{ ft}}.
This equation says that the ratio of the drawing length to the real length is the same as the scale ratio.

STEP 8

Rob chose A, which is the equation 14=x3\frac{1}{4} = \frac{x}{3}.

STEP 9

Rob flipped the relationship!
He put the real length (xx ft\text{ft}) in the numerator and the drawing length (3 cm\text{3 cm}) in the denominator, which doesn't match the scale proportion where the drawing length is in the numerator and the real length is in the denominator.

STEP 10

The correct equation is 14=3x\frac{1}{4} = \frac{3}{x}, which is option C.

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