If two triangles are similar, what is the perimeter of the

Question

If two triangles are similar, what is the perimeter of the smaller one?

(1) The sum of the perimeters of both triangles is 30
(2) The ratio is the measures of corresponding sides is 2:3

metallicafan · Answer

C

Let's check:

(1) The sum of the perimeters of both triangles is 30
Based on the fact that they are similar, let's suppose both are equilateres.
So, there could be different combinations of perimeters whose sum could be 30.
12 + 18 = 30
6 + 24 = 30
3 + 27 = 30
As you can see, there are different combinations of perimeters that could give us the desired result.
INSUFFICIENT.

(2) The ratio is the measures of corresponding sides is 2:3
Also, it happens the same. There are different combinations whose ratio is 2:3.
Let' see:
2 and 3 = 2:3
4 and 6 = 2:3
INSUFFICIENT

But in (1) and (2):
First, we must look for a combination whose ratio is 2:3
In other words: 2x:3x (x is a constant)
Also, the sum of the elements in this combination must be 30.
2x + 3x = 30
5x = 30
x = 6

The smaller perimeter is 2x = 12

SUFFICIENT

I think I deserve kudos 8-)

Bunuel · Answer

Let the sides of a smaller triangle be  a ,  b , and  c  and the sides of larger triangles  A ,  B , and  C  respectively. As triangles are similar then their sides are in same ratio:  \frac{a}{A}=\frac{b}{B}=\frac{c}{C} .

From above:  the perimeter of similar triangles is in the same ratio as their sides  -->  \frac{p}{P}=\frac{a}{A}=\frac{b}{B}=\frac{c}{C}

Question:  p=a+b+c=?

(1)  p+P=30 , clearly insufficient to calculate  p .

(2)  \frac{p}{P}=\frac{a}{A}=\frac{b}{B}=\frac{c}{C}=\frac{2}{3} , also insufficient to  p .

(1)+(2)  p+P=30  and  \frac{p}{P}=\frac{2}{3}  -->  P=\frac{3p}{2}  -->  p+P=p+\frac{3p}{2}=30  -->  p=12 . Sufficient.

Answer: C.

agnok · Answer

Thanks for the explanation.. Kudos given

saxenashobhit · Answer

if side of triangle is x, y,z. 
1. Sum of perimeter of two triangles will not help find the value
2. Ratio alone will not give unique value

Combining x+y+z +  \frac{2}{3}  (x+y+z) = 30

We can find x+y+Z by above so we can find perimeter. No need to solve.

Hence C

BlitzHN · Answer

1) x+y+z + n(x+y+z) = 30
we dont know n and hence not suff

2) we know n for above but, we dont know the sum

1 + 2 => solve... SUFF

pratikdas007 · Answer

This can be solved in much less than 2 minutes

Let P be the perimeter of the smaller triangle and then k be the ratio of the sides 
then KP is the perimeter of the larger triangle where K > 1

from (1) P + PK = 30

two variables , 1 equation , no solution

from (2) K = 1.5 ---> (3/2)

From (1) and (2) we have P = 30/2.5 = 12

Hence answer is C

Raths · Answer

yes...should be C...

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