Given that lmnk is a rhombus, km+ln=8, and the area of klmn is 6. find kl.

  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

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step-by-step explanation:

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