Answer:
The area of triangle ACE before dilation is: 30 square inches
Explanation:
We know that when an object is dilated by a scale factor, it gets reduced, stretched, or remains the same, depending upon the value of the scale factor.
- If the scale factor > 1, the image is enlarged
- If the scale factor is between 0 and 1, it gets shrunk
- If the scale factor = 1, the object and the image are congruent
The length of the image can be determined by multiplying the length of the original point by a certain scale factor.
Given that after triangle ACE is dilated by a factor of 6, it has an area of 180 square inches.
Thus, it means the dilated area is 6 times the area before dilation.
Let x be the pre-dilation area
As the dilated area is 6 times the area before dilation, so
6x = 180
divide both sides by 6
6x/6 = 180/6
x = 30 square inches.
Therefore, the area of triangle ACE before dilation is: 30 square inches