A square has a side length of 36 feet. this square is dilated by a scale factor of 2/3 to create a new square. what is the side length of the new square?
Answer:
the side length of the new square is, 24 feet
Step-by-step explanation:
Scale factor(k) is defined as the ratio of the dilated image to the Pre-image.
⇒ \(k = \frac{\text{Dilated image}}{\text{Pre-image}}\)
As per the statement:
A square has a side length of 36 feet. this square is dilated by a scale factor of 2/3
⇒Side length of the Pre-image square = 36 feet and k = 2/3
By definition we have;
\(\frac{2}{3} = \frac{\text{New side length of the dilated image of square}}{36}\)
Multiply both sides by 36 we have;
\(\frac{2}{3} \cdot 36=\text{New side length of the dilated image of square}\)
Simplify:
\(\text{New side length of the dilated image of square} = 24\) feet
therefore, the side length of the new square is, 24 feet