31. The square and the equilateral trianglebelow have the same perimeter. Write andsolve an equation that can be used to find

Comments (3) on “31. The square and the equilateral trianglebelow have the same perimeter. Write andsolve an equation that can be used to find”

1. x < 5.1

   Step-by-step explanation:

   Let's define:

   α: opposite angle to side 8 on the left triangleβ: the angle between sides 8 and 10 on the left trianglex: missing side of both triangles

   Using Law of Sines we can find x, as follows:

   10/sin(95°) = 8/sin(α)

   sin(α) = sin(95°)*8/10

   α = arcsin(0.8) = 53.13°

   β = 180° - 95° - 53.13° = 31.87°

   x/sin(β) = 10/sin(95°)

   x = 10/sin(95°)*sin(31.87°)

   x = 5.3

   On the other hand, we know that the addition of the two shorter sides of a triangle must be greater than the long side of the triangle. Therefore:

   8 + 5.3 > 3x - 2

   Solving:

   8 + 5.3 + 2 > 3x  

   15.3/3 > x

   5.1 > x

   or

   x < 5.1

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2. (6 cm) or 36 cm.

   Step-by-step explanation:The perimeter of a regular hexagon is just the sum of all 6 sides. Because it's a regular hexagon, the perimemter is just six times one side (6 cm) or 36 cm.

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3. help me first plz and get 30points

   Step-by-step explanation:

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