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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?

Respuesta :

Answer:

Ratio of perimeters = 7 : 9

Step-by-step explanation:

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

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

[tex]\text{Therefore, the ratio of the perimeters of the two triangles }\\\text{will be the same as the scale factor : }\frac{7}{9}[/tex]

Answer

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, [tex]\frac{7}{9}[/tex]

Each side of a image triangle is [tex]\frac{7}{9}[/tex] 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, [tex]\frac{7}{9}[/tex]