The scale factor for two similar triangles is 4 : 3. The perimeter of the smaller triangle is 12. What is the perimeter of the larger triangle?
( 4 / 3 ) * 12 = 48 / 3 = 16
To find the perimeter of the larger triangle, we need to use the scale factor provided.
First, let's determine the scale factor between the two triangles by comparing their corresponding sides. The scale factor is given as 4:3, which means that for every 4 units on the smaller triangle, there are 3 units on the larger triangle.
Next, we'll use the scale factor to find the length of the corresponding side on the larger triangle. Since the perimeter is the sum of all the sides, we need to multiply the length of each side of the smaller triangle by the scale factor to find the corresponding side on the larger triangle.
The perimeter of the smaller triangle is given as 12. Since a triangle has three sides of equal length in order to have a perimeter of 12, each side of the smaller triangle would be 4 units long (12 divided by 3).
Now, we can use the scale factor of 4:3 to find the length of each side of the larger triangle. Since the smaller triangle has sides of length 4, we can multiply 4 by the scale factor of 3 to get the length of each side of the larger triangle.
4 (length of side on smaller triangle) * 3 (scale factor) = 12 (length of side on larger triangle)
Therefore, each side of the larger triangle is 12 units long. Since a triangle has three equal sides, the perimeter of the larger triangle is 3 times the length of each side, which is:
3 (number of sides) * 12 (length of each side) = 36.
Hence, the perimeter of the larger triangle is 36 units.