iwo wrote:

there are two triangles whose vertices have same angles. If area of one triangle is twice the area of the other triangle, and the base of the smaller triangle is s, and base of the larger triangle is S, then what is S, in terms of s?

√2/2 s

√3/2 s

√2 s

√3 s

2 s

vertices have same angles <-- that tells us we are dealing with equilateral triangles with 60 degrees for each angle, so the height will be split with the 30-60-90 degree and will be 1/2*base* √3

i get A (although not 100% sure) please confirm

so lets start with the larger triangle

area = 1/2bh, stem tells us base is big S

area =

1/2 S * (√3)/2 S
smaller triangle

area = 1/2bh, base is little s

area =

1/2 s * (√3)/2 s
since area for larger triangle is twice that of the smaller

than

S * (√3)/2S =

1/2 s * (√3)/2s
solving for S (multiply inverse 2/√3 on both sides to clear LHS)

S^2 = √3/4 s^2 * 2/√3

S^2 = s^2 * 2/4

and take the sqrt on both sides:

S = s * √(1/2)

S = s * √2/2