SOLUTION: The lengths of the sides of a triangle are 5, 6, and 7. If the perimeter of a similar triangle is 36, what is the length of the shortest side of the similar triangle? A) 5 B) 4

Question 1030333: The lengths of the sides of a triangle are 5, 6, and 7. If the perimeter of a similar triangle is 36, what is the length of the shortest side of the similar triangle?
A) 5
B) 4
C) 6
D) 10
Thanks!!
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
The lengths of the sides of a triangle are 5, 6, and 7 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 = 10
6x = 6*2 = 12
7x = 7*2 = 14

So the original triangle has sides 5,6,7
The new triangle (simlar to the old one) has sides 10,12,14

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

--------------------------------------------

Final Answer: D) 10
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