Answer:
The ratio of the perimeters is 3
The ratio of the areas is 9
Step-by-step explanation:
Given:
Dilate a triangle with vertices (0, 0), (0, 2), and (2,0) using the scale factor k = 3.
To Find:
What is the value of the ratio (new to original) of the perimeters? the areas?
Solution:
What is the value of the ratio (new to original) of the perimeters?
Since, two figures are similar, then the ratio of its perimeters is equal to the scale factor
Let the following be:
k ⇒ the scale factor
x ⇒ the perimeter of the new triangle
y ⇒ the perimeter of the original triangle
Knowing that:
k = x/y
Thus:
k = 3
Now Substitute:
x/y = 3
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What is the value of the ratio (new to original) of the areas?
Since, two figures are similar, then the ratio of its areas is equal to the scale factor squared.
k ⇒ the scale factor
x ⇒ the area of the new triangle
y ⇒ the area of the original triangle
k ² = x/y
Since,
z = 3
Then,
x/y = 3 ²
3 ² means to 3 × 3
x/y = 9
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Kavinsky
