Question 389532: I am having trouble with this problem on this take home test that is due soon. The problem is: Two triangles are similar. The lengths of the sides of the smaller triangle are 4, 6, 7. The longest side of the larger triangle is 21. What is the perimeter of the larger triangle?
I know the perimeter of the smaller triangle is 17. But how does that help me find out the perimeter of the larger triangle when the only information I have is that they are similar and its largest side is 21? This question is multiple choice and I know I can cross out answer 1) 17 and answer 2)18. The last two answers are 42 and 51 and I just don't understand how it would be either. Can you please help!?
Found 2 solutions by mananth, josmiceli:
Answer by mananth(16946)   (Show Source):
You can put this solution on YOUR website! Two triangles are similar. The lengths of the sides of the smaller triangle are 4, 6, 7. The longest side of the larger triangle is 21. What is the perimeter of the larger triangle?
Since the triangles are congruent
the coressponding sides are congruent.
...
Largest side of larger triangle = 21.
this is 3 times the largest side of the smaller triangle.
..
The sides of the larger triangle
4*3 = 12
6*3=18
7*3=21
Total 51 the perimeter
...
m.ananth@hotmail.ca
Answer by josmiceli(19441)  (Show Source):
You can put this solution on YOUR website! if the larger triangle is similar, it's sides will be in the same
ratios as the smaller triangle, namely 4:6:7
The longest side of the larger triangle corresponds to
the longest side of the smaller triangle.
Suppose I call the sides of the larger triangle  , , and 
I can say
(1) 
(2) 
In (2), I can solve for
Now I can plug this into (1)
So, the sides of the larger triangle are  , , and
Notice this is 3 x  , 3 x  , and 3 x 
The larger triangle is "scaled up" by a factor of 3
The perimeter is 
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