Question

1 here is a scale drawing of a swimming pool where 1 cm represents 1 m. image of a blue rectangle a. how long and how wide is the actual swimming pool? b. will a scale drawing where 1 cm represents 2 m be larger or smaller than this drawing? c. make a scale drawing of the swimming pool where 1 cm represents 2 m.

Explanation:

Part a

Step1: Measure the drawing's length and width.

Assume the scale drawing's length is \( L_{draw} \) cm and width is \( W_{draw} \) cm. (We can visually estimate or measure: let's say the drawing's length is 5 cm and width is 3 cm for example, but in reality, we measure the given rectangle. Let's assume actual measurement: length of drawing is 5 cm, width is 3 cm. Since 1 cm = 1 m, actual length \( L_{actual} = L_{draw} \times 1 \) m, actual width \( W_{actual} = W_{draw} \times 1 \) m.

Step2: Calculate actual dimensions.

If \( L_{draw} = 5 \) cm, \( L_{actual} = 5 \times 1 = 5 \) m. If \( W_{draw} = 3 \) cm, \( W_{actual} = 3 \times 1 = 3 \) m. (Note: The actual measurement of the drawing's length and width may vary, but the method is to multiply the drawing's length/width in cm by 1 m/cm.)

Step1: Understand scale factor.

The original scale is 1 cm : 1 m, new scale is 1 cm : 2 m. A larger scale factor (in terms of real - world per cm) means that for the same actual length, the length on the drawing will be smaller. For example, if the actual length is 2 m, in the original scale, the drawing length is \( \frac{2}{1}=2 \) cm; in the new scale, the drawing length is \( \frac{2}{2} = 1 \) cm.

Step2: Compare the two drawings.

Since for the same actual size, the length on the new - scale drawing (1 cm represents 2 m) is shorter than the length on the original - scale drawing (1 cm represents 1 m), the new scale drawing will be smaller.

Step1: Recall actual dimensions.

From part (a), let the actual length be \( L \) m and actual width be \( W \) m. For example, if \( L = 5 \) m and \( W = 3 \) m.

Step2: Calculate new drawing dimensions.

Using the new scale (1 cm represents 2 m), the length of the new drawing \( l_{new}=\frac{L}{2} \) cm and the width of the new drawing \( w_{new}=\frac{W}{2} \) cm. If \( L = 5 \) m, \( l_{new}=\frac{5}{2}=2.5 \) cm; if \( W = 3 \) m, \( w_{new}=\frac{3}{2} = 1.5 \) cm.

Step3: Draw the rectangle.

Draw a rectangle with length \( l_{new} \) cm and width \( w_{new} \) cm.

Answer:

Suppose the scale - drawing length is \( l \) cm and width is \( w \) cm. The actual length is \( l\times1 = l \) m and the actual width is \( w\times1 = w \) m. For example, if the drawing length is 5 cm and width is 3 cm, the actual length is 5 m and the actual width is 3 m.

Part b