HELP with a 2u PAST TRIAL Question. Please. (1 Viewer)

[Mr_Kap]

The question (I have the two triangles drawn in my working out):

My working out:

Why was my answer getting the ratio of a:b as 5:7, when the answers said it was 7:5.
Any help would be greatly appreciated.

 

[kawaiipotato]

I'll check your working out but what I just did was:
let angle O = B
Area OCD = 1/2 a^2 sinB
Area OAB = 1/2 (a+b)sinB
Area OCD / Area OAB = 49/144
so: a^2/(a+b)^2 = 49/144
Square rooting, a/(a+b) = 7/12
12a = 7a+7b
5a = 7b
a/b = 7/5
So, a:b = 7:5

 

[kawaiipotato]

And just checked you're right until the very last line.
98b = 70a
dividing: a/b = 98/70
So, a:b = 7:5

 

[Mr_Kap]

And just checked you're right until the very last line.
98b = 70a
dividing: a/b = 98/70
So, a:b = 7:5

Thx. Just made a stupid error at the end.