Question

In rectangle ABCD, point L lies on diagonal
BD
. Points K and M lie on segments
BC
and
CD
respectively. It ends up that quadrilateral LKCM is a square. Given AD = a and AB = b, find the length of the side of square LKCM.

Answer 1

Answer:

  ab/(a+b)

Step-by-step explanation:

Without loss of generality, we can put point C at the origin and define line BD by the equation ...

  x/a +y/b = 1

Points (x, y) fall on the line BD, and we have point L where x=y. That value of x, the square's side length, will satisfy ...

  x/a +x/b = 1 . . . . . fill in x=y in the equation

  x(a+b)/ab = 1 . . . .factor out x, add 1/a+1/b

  x = ab/(a+b) . . . . solve for x

The length of the side of the square is ab/(a+b).