Question

3 you can also change the scale on a scale drawing to make the representation larger. draw heather’s garden using a scale of 1 cm : 4 m. 4 would a scale drawing of a door with a scale of 1 in. : 3 ft be longer or shorter than a scale drawing of the same door with a scale of 1 in. : 6 ft? why?

Explanation:

Step1: Understand Scale Meaning

A scale of \(1\) in. : \(3\) ft means \(1\) inch on drawing represents \(3\) feet in real. A scale of \(1\) in. : \(6\) ft means \(1\) inch on drawing represents \(6\) feet in real.

Step2: Compare Representation for Same Real Length

Let the real length of the door be \(L\) feet. For scale \(1\) in. : \(3\) ft, drawing length \(d_1=\frac{L}{3}\) inches. For scale \(1\) in. : \(6\) ft, drawing length \(d_2 = \frac{L}{6}\) inches. Since \(\frac{L}{3}>\frac{L}{6}\) (for positive \(L\)), the drawing with scale \(1\) in. : \(3\) ft is longer. So the drawing with \(1\) in. : \(6\) ft is shorter than with \(1\) in. : \(3\) ft. Because a larger real length per inch on the drawing (6 ft vs 3 ft) means the same real door length will be represented by a shorter length on the drawing.

Answer:

A scale drawing of a door with a scale of \(1\) in. : \(6\) ft would be shorter than a scale drawing of the same door with a scale of \(1\) in. : \(3\) ft. This is because in the \(1\) in. : \(6\) ft scale, each inch on the drawing represents a longer real - world length (6 feet) compared to the \(1\) in. : \(3\) ft scale (where each inch represents 3 feet). So, for the same actual door length, the number of inches needed to represent it in the \(1\) in. : \(6\) ft scale is less (since \(\text{drawing length}=\frac{\text{actual length}}{\text{length represented per inch}}\)), resulting in a shorter drawing.