MIKE HAS 2 MATS THAT ARE IN THE SHAPE OF TRIANGLES THE SCALE FACTOR OF THE 2 TRIANGULAR MATS IS 7/9 WHAT IS THE RATIO OF THE PERIMETERS?

7/9

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To find the ratio of the perimeters of the two triangular mats, we first need to understand the concept of the scale factor. The scale factor is the ratio of the lengths of corresponding sides of two similar shapes.

In this case, Mike has two triangular mats, and the scale factor between them is given as 7/9. This means that the lengths of corresponding sides of the two triangles are in the ratio of 7:9.

Let's assume the first triangle has side lengths of a, b, and c, and the second triangle has corresponding side lengths of x, y, and z.

Since the scale factor between the two triangles is 7/9, we can write the following equations:

x = (7/9)a
y = (7/9)b
z = (7/9)c

Now, let's find the ratio of the perimeters of the two triangles.

The perimeter of a triangle is the sum of its three sides. So, the perimeter of the first triangle is given by:

Perimeter of the first triangle = a + b + c

Similarly, the perimeter of the second triangle is:

Perimeter of the second triangle = x + y + z

Substituting the values of x, y, and z in terms of a, b, and c, we get:

Perimeter of the second triangle = (7/9)a + (7/9)b + (7/9)c

To find the ratio of the perimeters, we divide the perimeter of the first triangle by the perimeter of the second triangle:

Ratio of the perimeters = (a + b + c) / ((7/9)a + (7/9)b + (7/9)c)

Simplifying this expression, we get:

Ratio of the perimeters = 9/7

Therefore, the ratio of the perimeters of the two triangular mats is 9:7.