Respuesta :
If two shapes are similar, it means that you can obtain one from the other by scaling it by a certain factor [tex] k [/tex] (you can think of this as of "zooming" the shape in or out).
In particular, this implies that all the side lengths are multiplied by the same amount.
Now, the original hexagon has two sides of 4, and all other sides are different. This implies that, if we multiply all side lengths by the same number, we will still have two sides with equal lengths, and all other sides will have different lengths.
So, the 2 sides with length 3 must come from the two sides with length 4, after scaling. In particular, this also implies that the scaling factor is
[tex] 4k = 3 \iff k = \dfrac{3}{4} [/tex]
So, the perimeter of the new hexagon is the sum of its sides, which in turn are the old sides multiplied by the scaling coefficient:
[tex] \frac{3}{4}(4+3+4+6+8+9) = \dfrac{3}{4}\cdot 34 = 25.5 [/tex]
The two hexagons are similar. The perimeter of a similar hexagon with two sides of length 3 is 25.5 units.
Given :
Sides of hexagon 4,3,4,6,8, and 9.
What are similar shapes?
If two shapes are similar, that means that we can obtain one from the other only by scaling it by a certain factor.
In particular, this implies that all the side lengths are multiplied by the same amount.
Now, the original hexagon has two sides of 4, and all other sides are different.
This implies that, if we multiply all side lengths by the same number, we will still have two sides with equal lengths, and all other sides will have different lengths.
So, the 2 sides with length 3 must come from the two sides with length 4, after scaling.
In particular, this also implies that the scaling factor is
[tex]\rm 4k = 3 \\\\k = \dfrac{3}{4}[/tex]
Hence, The perimeter of the new hexagon is the sum of its sides, which in turn are the old sides on multiplying by the scaling its coefficient:
[tex]\rm= \dfrac{3}{4}(4+3+4+6+8+9)=\dfrac{3}{4} \times34=25.5[/tex]
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