The scale factor of two similar triangles is 2/5. if the perimeter of the small triangles is 80 cm, what is the perimeter of the large triangle?

5/2 = x/80

Solve for x.

200 cm

x=200

To find the perimeter of the larger triangle, we need to understand that the scale factor applies to all sides of the triangles.

First, let's determine the scale factor between the two triangles. The scale factor is given as 2/5, which means that the corresponding sides of the larger triangle are 2/5 times the length of the corresponding sides of the smaller triangle.

Let's denote the lengths of corresponding sides of the small triangle as a, b, and c, and the corresponding sides of the large triangle as A, B, and C.

Since the perimeter of the small triangle is given as 80 cm, we have:

Perimeter of small triangle = a + b + c = 80 cm

Now, we can use the scale factor to express the lengths of the sides of the larger triangle in relation to the smaller triangle:

A = (2/5) * a
B = (2/5) * b
C = (2/5) * c

To find the perimeter of the large triangle, we need to calculate A + B + C:

Perimeter of large triangle = (2/5) * a + (2/5) * b + (2/5) * c
= (2/5) * (a + b + c) [factor out 2/5]
= (2/5) * 80 cm [substitute the perimeter of the small triangle]
= 32 cm

Therefore, the perimeter of the large triangle is 32 cm.