Answer: 15
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Step-by-step explanation:
Going from design 1 to design 2, we add on 3 triangles. This is because the triangle in design 1 has 3 exterior sides to form its perimeter.
Going from design 2 to design 3, we add on 6 triangles
Going from design 3 to design 4, we add on 9 triangles
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Note the pattern of triangles we add on each round: 3, 6, 9
This is the set of multiples of 3. Each number is increased by 3. The next design will have us add 12 triangles to the exterior of design 4. Then the next round has us add on 15 triangles to the outside.
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Going from design 4 to design 5, we add on 12 triangles
Going from design 5 to design 6, we add on 15 triangles
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Check out the attached image below for what designs 5 and 6 will look like. Note the use of color coding to help see how the figures build up from step to step. There are 15 orange triangles along the outside in design 6.