Answer:
KL = √10
Step-by-step explanation:
The product of KM and LN is twice the area, so is 12. This gives a quadratic in one or the other of those variables:
KM(8 -KM) = 12 . . . . the product of diagonals is twice the area
KM² -8·KM +12 = 0 . . . . rearrange to standard form
(KM -2)(KM -6) = 0 . . . . factor
KM = 2 or 6 . . . . values that make the factors zero
LN = 6 or 2 . . . . corresponding values of LN
The Pythagorean theorem tells you the side length from the diagonals:
KL² = (KM/2)² +(LN/2)² = 1² +3² = 10
KL = √10 . . . . . take the square root
