The Table Below Gives The Dimensions Of A Painting And A Scale Drawing Of The Painting. Find The Scale Factor Of The Drawing. (The Scale Factor To Get The Drawing From The Painting.) Write Your Answer As A Fraction In Simplest
**The Table Below Gives the Dimensions of a Painting and a Scale Drawing of the Painting: Find the Scale Factor of the Drawing**
A scale factor is a number that represents the ratio of the size of a scaled object to the size of the original object. In other words, it is the factor by which the dimensions of the original object are multiplied to obtain the dimensions of the scaled object.
Understanding the Problem
The table below gives the dimensions of a painting and a scale drawing of the painting.
| Length (cm) | Width (cm) | |
|---|---|---|
| Painting | 25 | 30 |
| Scale Drawing | 5 | 6 |
Q: What is the scale factor of the drawing?
A: To find the scale factor, we need to divide the dimensions of the scale drawing by the dimensions of the painting.
Step 1: Find the Scale Factor for Length
To find the scale factor for length, we divide the length of the scale drawing (5 cm) by the length of the painting (25 cm).
Scale factor for length = 5 cm / 25 cm = 1/5
Step 2: Find the Scale Factor for Width
To find the scale factor for width, we divide the width of the scale drawing (6 cm) by the width of the painting (30 cm).
Scale factor for width = 6 cm / 30 cm = 1/5
Q: What is the scale factor of the drawing?
A: Since the scale factor for both length and width is the same (1/5), the scale factor of the drawing is 1/5.
Q: What does the scale factor represent?
A: The scale factor represents the ratio of the size of the scaled object (the scale drawing) to the size of the original object (the painting). In this case, the scale drawing is 1/5 the size of the painting.
Q: How is the scale factor used in real-life applications?
A: The scale factor is used in various real-life applications, such as:
- Architecture: to create scale models of buildings and structures
- Engineering: to design and build scaled prototypes of machines and mechanisms
- Art: to create scaled drawings and paintings of objects and scenes
- Education: to teach students about proportions and scaling
Q: Can the scale factor be used to find the dimensions of the original object?
A: Yes, the scale factor can be used to find the dimensions of the original object. If we know the dimensions of the scaled object and the scale factor, we can multiply the dimensions of the scaled object by the scale factor to obtain the dimensions of the original object.
Q: What is the relationship between the scale factor and the ratio of the areas?
A: The scale factor is related to the ratio of the areas of the two objects. If the scale factor is 1/n, then the ratio of the areas is 1/n^2.
Conclusion
In conclusion, the scale factor is a fundamental concept in mathematics that represents the ratio of the size of a scaled object to the size of the original object. It is used in various real-life applications and can be used to find the dimensions of the original object.