Help please? I'm confused!?

Let y = the small base and x = the large base.

Draw the two altitudes from each corner of the small base.

The large base will then be made up of a section of length y

and two end sections each of length (x - y)/2.

Draw a diagonal which is length x. Make this the hypotenuse

of a triangle which has legs of length y and [y + (x - y)/2].

Therefore, by Pythagoras,

x^2 = y^2 + [y + (x - y)/2]^2

= y^2 + [y + x/2 - y/2]^2

= y^2 + {x/2 + y/2)^2

= y^2 + [(x + y)/2]^2

= y^2 + (x + y)^2 / 4

Multiply through by 4 :

4x^2 = 4y^2 + (x + y)^2

= 4y^2 + x^2 + 2xy + y^2

Simplify :

3x^2 = 5y^2 + 2xy

Divide through by xy :

3x/y = 5y/x + 2

3(x/y) = 5(y/x) + 2

3(x/y) = 5 / (x/y) + 2

Let x/y = k

so, 3k = 5/k + 2

Multiply through by k :

3k^2 = 5 + 2k

Rearrange :

3k^2 - 2k - 5 = 0

Factorise :

(k + 1)(3k - 5) = 0

Thus, k = -1 or 5/3

That is, x/y = -1 or 5/3

But x/y cannot be negative, so x/y = 5/3, or x:y = 5:3.