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
To find the perimeter of the larger triangle when given the scale factor and the perimeter of the smaller triangle, you can follow these steps:
Step 1: Determine the scale factor.
Given that the scale factor for the two similar triangles is 4:3, we can express it as a ratio: 4/3.
Step 2: Find the ratio of perimeters.
Since the scale factor applies to all corresponding sides, it also applies to the perimeter. It means that the ratio of the perimeters of the two triangles is the same as the scale factor ratio.
So, we can set up the following proportion:
Perimeter of smaller triangle / Perimeter of larger triangle = Scale factor
We know that the perimeter of the smaller triangle is 12, so let's substitute that in:
12 / Perimeter of larger triangle = 4/3
Step 3: Solve for the perimeter of the larger triangle.
To find the perimeter of the larger triangle, we need to isolate the variable (Perimeter of larger triangle) on one side of the equation. We can do this by cross-multiplying and then dividing:
12 * 3 = 4 * Perimeter of larger triangle
36 = 4 * Perimeter of larger triangle
Now, divide both sides of the equation by 4 to solve for the perimeter of the larger triangle:
(36 / 4) = (4 * Perimeter of larger triangle) / 4
9 = Perimeter of larger triangle
Therefore, the perimeter of the larger triangle is 9.