Question

Mike has 2 mats that are in the shape of triangles. The scale factor of the two triangular mats is 7 / 9. What is the ratio of the perimeters?

Answer 1

As per the statement: Mike has 2 mats that are in the shape of triangles.

It is also given that the scale factor of the two triangles mats is,
`(7)/(9)`

Each side of a image triangle is
`(7)/(9)` times the length of the corresponding side of the pre image triangle.

Since, each side is scaled by a factor of 7/9.

Perimeter of a triangle defined as the sum of all the three sides of a triangle.

⇒ the sum of the three side side of a image triangle will also be scaled by a factor of 7/9 times the perimeter of a pre-image triangle.

Therefore, the ratio of the perimeters is,
`(7)/(9)`

Answer 2

Ratio of perimeters = 7 : 9

Explanation:

Each side of the smaller triangle is 7 by 9 times the length of the corresponding side of the large triangle.

`\text{Now, Since each side of the triangle is scaled by a factor of }(7)/(9)\\\text{So, sum of the lengths of the three sides will also be scaled by a factor of }(7)/(9)`

`\text{Therefore, the ratio of the perimeters of the two triangles }\\\text{will be the same as the scale factor : }(7)/(9)`