Question

6 the drawing at the right is a plan for a parking lot. each unit of length in the drawing is 0.5 cm. the actual parking lot has a perimeter of 84 m. draw another scale drawing of the parking lot using a scale from the parking lot to the new drawing of 2 m to 0.5 cm. justify why your drawing is accurate.

Explanation:

Step1: Find the scale - factor relationship

The new scale is 2 m to 0.5 cm. This means 1 m in actual corresponds to $\frac{0.5}{2}=0.25$ cm in the new drawing.

Step2: Calculate the perimeter in the new drawing

The actual perimeter is 84 m. In the new drawing, the perimeter $P_{new}=84\times0.25 = 21$ cm.

Step3: Analyze the original drawing's scale

The original scale has each unit of length in the drawing as 0.5 cm, but we don't need its details for the new - scale drawing.

Step4: Draw the new scale - drawing

To draw the new scale - drawing, we first need to know the shape of the parking lot. Let's assume the parking lot is a rectangle (if it's a more complex shape, we can break it into smaller rectangles or other basic shapes). If we assume the parking lot has length $l$ and width $w$ such that $2(l + w)=84$ m (perimeter formula for rectangle), then $l + w = 42$ m. In the new drawing, $l_{new}+w_{new}=42\times0.25 = 10.5$ cm. We can choose values for $l_{new}$ and $w_{new}$ such that their sum is 10.5 cm (e.g., $l_{new}=6$ cm and $w_{new}=4.5$ cm) and draw the rectangle.

Step5: Justify the accuracy

We used the scale factor of 0.25 cm per 1 m to convert the actual - world measurements to the drawing measurements. The perimeter calculation and the side - length calculations are based on this scale factor, ensuring that the new drawing is in proportion to the actual parking lot.

Answer:

Draw a rectangle (or the appropriate shape based on the actual parking - lot shape) with a perimeter of 21 cm using the scale 1 m = 0.25 cm. Justify by showing that all measurements are calculated using the scale factor of 0.25 cm per 1 m.