cyan storm
Given a rectangle ABCD where |AB| : |BC| = 2 : 1.
On its sides AB, BC, CD, DA are given by
K, L, M, N so that KLMN is a rectangle,
in which |KL| : |LM| = 3 : 1. Calculate the ratio
of the areas of the rectangles ABCD and KLMN.
My process:
AB = 2x, CD = x, MN = 3y, KN = y
AKN is similar to DNM, k = 3 (hypotenuse of DNM is 3y and hypotenuse of AKN is y)
DN = 3AK, DM = 3AN
hence 3AN + AK = 2x and AN + 3AK = x
so x = 8AK, AN = 5AK
S(ABCD) = x * 2x = 8AK * 16AK = 128AK²
NK² = AN² + AK² = 25AK² + AK² = 26AK²
S(KLMN) = 3 * NK² = 78AK²
S(ABCD) : S(KLMN) = 128:78 = 64:39
I find the solution a bit weird. Could someone please check it and tell if its correct or wrong?
civic mantle