Drawing in different scales :
The dimensions on a scale drawing can be multiplied by a scale factor to create a new scale drawing.
An original drawing can be increased or decreased by a scale factor to create Scale Drawing 1.
Scale Drawing 1 can be increased or decreased by a scale factor to create Scale Drawing 2.
Scale Drawing 2 is also a scale drawing of the original.
Read the passage carefully and answer the questions given below :
A scale drawing of a meeting hall is drawn on centimeter grid paper as shown. The scale is 1 cm:3 m.
Suppose you redraw the rectangle on centimeter grid paper using a scale of 1 cm:6 m. In the new scale, 1 cm represents more than 1 cm in the old scale.
The measurement of each side of the new drawing will be half as long as the measurement of the original drawing.
Question 1 :
Draw the rectangle for the new scale 1 cm:6 m.
Question 2 :
Find the actual length and width of the hall using the original scale. Then find the actual length and width of the hall using the new scale. How do you know your answers are correct ?
Step 1 :
Find the actual length and width of the hall using original scale.
Length is 8 × 3 = 24 m and the width is 6 × 3 = 18 m.
Step 2 :
Find the actual length and width of the hall using new scale.
Length is 4 × 6 = 24 m and the width is 3 × 6 = 18 m.
The answers are correct, because both scales give the same actual lengths.
Question 3 :
Explain how you know that there is a proportional relationship between the first and second drawings.
The first drawing using the original scale and the second drawing using the new scale are similar figures.
Because, both of them are rectangles.
There is a fact that there is always a proportional relationship between two similar figures.
Hence, there is a proportional relationship between the first and second drawings
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