Question 1030333
<font color=blue>The lengths of the sides of a triangle are 5, 6, and 7</font> is given to us. 


Let x be any positive number. So x > 0.


Any similar triangle to this given one will have side lengths of 5x, 6x, 7x. Each side is simply the original side times x.


Let's add up the sides of the new triangle and set them equal to the perimeter


5x+6x+7x = 36


then let's solve for x


5x+6x+7x = 36


18x = 36


18x/18 = 36/18


x = 2


So if we multiply every side of the original triangle by x = 2, then we get these new sides


5x = 5*2 = <font color=green>10</font>
6x = 6*2 = <font color=green>12</font>
7x = 7*2 = <font color=green>14</font>


So the original triangle has sides 5,6,7
The new triangle (simlar to the old one) has sides <font color=green>10</font>,<font color=green>12</font>,<font color=green>14</font>


Notice how adding up those new sides give
10+12+14 = 22+14 = 36
which is the perimeter we want


We can see that the shortest side of the new triangle is 10


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Final Answer: <font color=red size=5>D) 10</font>