Well, since we're dealing with similar triangles here, there has to be some type of common ratio between the lengths of both triangles since all the degree measures are the same. That common ratio is going to be S/s. Now,let's say that the height of the smaller triangle is h. If this is true then the height of the bigger triangle is going to be h times the ratio that we got before or h*S/s. Now just use the basic triangle area formulas:

Area of big triangle: (S*S/s*h)/2

Area of small triangle: hs/2

S^2*h/2s=2*sh/2

2s^2=S^2

S=sqrt(2)*s

These two triangles are similar. Therefore,

Area of Big Triangle/ Area of Small Triangle
(A1)/(A2)

=

S^2/s^2

or A1/A2 = S^2/s^2

we know that A1 = 2*A2

Therefore 2*A2/A2= S^2/s^2

or S = sqrt(2)*s

truplayer256 wrote: Now,let's say that the height of the smaller triangle is h. If this is true then the height of the bigger triangle is going to be h times the ratio that we got before or h*S/s.

Can you explain how you got the height of bigger triangle? I don't seem to understand the concept here

Just need to know a simple rule for this one.

If 2 triangles are similar and their sides are in the ratio a:b,then their areas are in the ratio ,a^2:b^2

Given : a^2:b^2 = 2:1,hence a:b = sqrt(2):1
Hence If the smaller triangle has side s the larger will be sqrt(2)s

Just mins back, i read the similarity chapter in detail. Now this prob seems to be a cake-walk. Thanks for explaining sanjana

sanjana wrote:Just need to know a simple rule for this one.

If 2 triangles are similar and their sides are in the ratio a:b,then their areas are in the ratio ,a^2:b^2

Given : a^2:b^2 = 2:1,hence a:b = sqrt(2):1
Hence If the smaller triangle has side s the larger will be sqrt(2)s

I dont understand.
I know that area = 1/2*B*H
so Trible A is two times the size of Triangle B

Where does the A^2, the ^2 come from??


if the big triangle is twice the area of the smaller triangle, would'nt small 2s = S ? where did the sqrt root come from??

nvm i think i got it, and u guys explained it quit thoroughly, i was just missing one peice of important information.

this site is helpful for people who are still not getting this : https://www.mathopenref.com/similartrianglesareas.html

so it pretty much comes down to that: the area of the two triangles are from small to big: s^2=area of small triangle, S^2=area of big triangle.

to help you see this, visit the site

Then the big triangle is TWICE the area of the small one, therefore: 2s^2=S^2, squared, you get the answer. See i dont know if I will get this question right because the wording is confusing, which is how these questions get people.