Two similar triangles have a scale factor of 5/3.
a) Find the perimeter ratio copy/original
b) Find the area ratio
copy/original
a) 5/3
b)10/6
To find the perimeter ratio between two similar triangles, you need to compare the lengths of the corresponding sides. Since the scale factor is given as 5/3, it means that every side of the copy triangle is 5/3 times the length of the corresponding side in the original triangle.
a) Perimeter ratio (copy/original):
To find the perimeter ratio, you need to add up all the sides of both the copy and original triangles. Let's say the copy triangle has sides a', b', and c', and the original triangle has sides a, b, and c.
The perimeter ratio is given by:
Perimeter ratio = (a' + b' + c') / (a + b + c)
Since the scale factor for all sides is 5/3, we can express the sides of the copy triangle in terms of the sides of the original triangle:
a' = (5/3) * a
b' = (5/3) * b
c' = (5/3) * c
Substituting these values into the perimeter ratio equation, we get:
Perimeter ratio = ((5/3) * a + (5/3) * b + (5/3) * c) / (a + b + c)
Simplifying the equation, we get:
Perimeter ratio = 5/3
Therefore, the perimeter ratio between the copy and original triangles is 5/3.
b) Area ratio (copy/original):
To find the area ratio between two similar triangles, you need to compare the areas of the triangles. Since the scale factor is given as 5/3, it means that the area of the copy triangle will be (5/3)^2 = 25/9 times the area of the original triangle.
Area ratio = Area of copy triangle / Area of original triangle
= (25/9)
Therefore, the area ratio between the copy and original triangles is 25/9.