Hi All, Happy New-Year to everyone.

I've attached below a diagram of the question. My attempts at it have left me stumped...

I have to find the length AB and length AB= x

I started this off by finding length AC using pythagoras and got AC= 5

Then I deduced that since AB= x, then the small length BC can be written as BC = x-5

Also, I can note that length CD= a

So,

[TEX](x-5)^2 = a^2 + 1^2[\TEX]

[TEX]a^2 = x^2 -10x - 24[\TEX]

[TEX]a^2 = (x-6)(x-4)[\TEX]

Hence,

[TEX]a = \pm\sqrt{6} or \pm\sqrt{4}[\TEX]

[TEX] a= 2.45 or 2[\TEX]

So, if CD = 2.45 or 2, then using pthagoras again we can now > calculate

[TEX]BC = \sqrt{2.45^2 + 1^2} = \sqrt{7}[\TEX]

Which would result in length AB = 5 + \sqrt{7} = 7.65[\TEX]

Using CD = 2 with the same above steps gives;

[TEX]BC = \sqrt{5}[\TEX] and AB = 7.24

However the answer is;

[TEX]AB= 4\sqrt{2} or 5.657[\TEX]

Where have i gone wrong? Thanks for the help.