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?

since perimiter is a linear measurement, the ratio of the perimeter equals the ratio of the sides

if x is the larger perimeter,
x/12 = 3/4
4x = 36
x = 9

If sides of a triangle are 3,4, and 5 with a scale factor of 3, what are lengths of the similar triang

To find the perimeter of the larger triangle, we can use the scale factor between the two triangles.

Since the scale factor is 4:3, this means that every side length of the larger triangle is 4 times the corresponding side length of the smaller triangle.

Given that the perimeter of the smaller triangle is 12, we need to determine the corresponding perimeter of the larger triangle.

Let's assume the perimeter of the larger triangle is P.

Since the scale factor is 4:3, this means that the corresponding perimeter of the larger triangle is 4 times the perimeter of the smaller triangle.

Therefore, we have:

P = 4 * 12 = 48

Hence, the perimeter of the larger triangle is 48.

To find the perimeter of the larger triangle, we need to determine the scale factor by comparing the corresponding sides of the two triangles.

Given that the scale factor is 4:3, we can express the lengths of the corresponding sides of the smaller and larger triangles as follows:

Let's assume the lengths of the corresponding sides of the smaller triangle are 4x and 3x.

Now, we know that the perimeter of a triangle is the sum of the lengths of all its sides. Therefore, the perimeter of the smaller triangle, which has sides of length 4x and 3x, is:

P1 = 4x + 3x = 7x

We also know that the perimeter of the smaller triangle is 12 units. Therefore, we can set up an equation:

7x = 12

To solve for x, divide both sides of the equation by 7:

x = 12/7

Now that we have the value of x, we can find the lengths of the sides of the larger triangle using the scale factor:

4x (side of the smaller triangle) = 4 * (12/7) = 48/7
3x (corresponding side of the larger triangle) = 3 * (12/7) = 36/7

Finally, to find the perimeter of the larger triangle, we add up the lengths of its sides:

P2 = (48/7) + (36/7) = 84/7 = 12

Therefore, the perimeter of the larger triangle is 12 units.