GMAtprep question

[mlane25269]

How do I solve?

[Nycgrl]

Area of bigger trangle A = 2 a(area of smaller triangle)

A/a= 2

all the three angles are equal therefore both the triangles are similar

A/a =S/s=2 =>S=2s

[smashinonions]

https://www.mathopenref.com/similartrianglesareas.html


for similar triangles,

side = Sqrt (area)

let s = a (area)
and S= A (area)

given,


A = 2a


also,

s / S = sqrt(a)/ sqrt(2a)

or S = Sqrt(2a) * s/ sqrt(a)

= Sqrt (2a) Sqrt (a) * s/ Sqrt (a) * sqrt (a) [simplification]

= sqrt (2) * s (ANS)

[AleksandrM]

smashonions,

Is this some sort of a rule?

for similar triangles,

side = Sqrt (area)


Can you elaborate. Thanks.

[egybs]

The rule is:

Where:
A1: area of similar triangle 1
A2: area of other similar triangle 2
L1: length of any side (the base) or height on triangle 1
L2: length of related side or height on triangle 2


A1/A2 = X

L1 = L2 * sqrt(X)

If you want the proof, let me know and I'll work out it for you.

[smashinonions]

the ratio of the sides of two similar triangles is equal to the sqrt of the ratio of their areas is the rule

which is if triangles A1 and A2 have sides S1 and S2 and areas Ar1 and Ar2 then,

S1 / S2 = Sqrt ( Ar1 / Ar2)

pls visit https://www.mathopenref.com/similartrianglesareas.html for more details

[AleksandrM]

Kool, thank you guys.

[rosh26]

Is there another way to solve the problem?

I'm just not understanding the solution above.

Thanks in advance.

[mlane25269]

I agree with rosh26!! I'm having trouble understanding the concept. Is this based on a formula because I haven't seen this concept covered in the official GMAT guide or any of the Kaplan resources I've looked at. Would this fall under geometry and how likely is something like this to appear on the real GMAT?

[AleksandrM]

If there are two similar triangles, one with Area = 8 the other one with Area = 2 the bigger angle has side S the smaller side s.

Say that side S is the base and = 4, which means that height is also 4.

Now, what is the measure of side s.

S/s = sqroot(Area/area)

4/s =sqroot(8/2)

s = 2.

I believe that this is how it's done, though I just learned this approach myself.

[rosh26]

but the answer is sqrt 2 (s) not 2s...

[AleksandrM]

That's because that is as far as you can simplify it.