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The area of parallelogram JKLM is 28 bar...

The area of parallelogram JKLM is 28 `bar(JK)=7`. If `bar(KN)` is perpendicular to `bar(ML)` and if N is the midpoint of `bar(ML)`, what is the perimeter of JKLM ?

A

`24.6302`

B

`23.25`

C

28

D

`31.596`

Text Solution

Verified by Experts

The correct Answer is:
A
Because JKLM is a parallelogram, opposite sides are equal and `bar(ML)=7`. Midpoint N divides that 7 into two equal pices of `(7)/(2)` each. The area of the parallelogram, which is equal to the base times the height, is given as 28, and because the base is 7, altitude `bar(KN)=4`. Put all this into the figure.

Use the Pythagorean theorem to determine the length of `bar(KL)`.
`bar(LN)^(2)+bar(KN)^(2)=bar(KL)^(2)`
`((7)/(2))^(2)+4^(2)=bar(KL)^(2)`
`(49)/(4)+16=bar(KL)^(2)`
`(49)/(4)+(64)/(4)=bar(KL)^(2)`
`(113)/(4)=bar(KL)^(2)`
`sqrt((113)/(4))=bar(KL)~~5.3151`
Now add all the sides of the parallelogram to find the perimeter : `7+7+5.3151=24.6302`.
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