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4 years ago

Given that LMNK is a rhombus, KM+LN=8, and the area of KLMN is 6. Find KL.

Mathematics

1 answer:

kirza4 [7]4 years ago

4 0

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

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Unfortunately I can't read your answer options properly. The copied text is just too messed up. But hopefully the step-by-step calculation will help you.

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Step-by-step explanation:

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