I have two similar triangles. The perimeter of the smaller triangle is 20. If a scale factor of 1 1/4 is used to dilate the triangle, what is the perimeter of the larger triangle?
Each side will be multiplied by 1.25, so the total perimeter will be multiplied by 1.25
20*1.25 =
To find the perimeter of the larger triangle, you need to understand how scales factors work in dilations.
A scale factor determines the ratio of corresponding side lengths between two similar figures. In this case, the scale factor is 1 1/4.
To find the perimeter, you will multiply the corresponding side lengths of the smaller triangle by the scale factor.
Given that the perimeter of the smaller triangle is 20, it means that the sum of all its side lengths is 20.
Let's assume the corresponding side lengths in the smaller and larger triangles are denoted by a and b (in some order).
Now, multiplying both a and b by the scale factor 1 1/4:
a * (5/4) + b * (5/4) = 20
The sum of the corresponding side lengths of the larger triangle will be 20.
Simplifying this equation:
5a/4 + 5b/4 = 20
Multiplying both sides of the equation by 4 to eliminate the fractions:
5a + 5b = 80
Dividing both sides of the equation by 5:
a + b = 16
Since the sum of the corresponding side lengths in the larger triangle is 16, the perimeter of the larger triangle is 16.