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Question

In Figure 5, the area of parallelogram JKLM is 28 and ¯¯¯¯¯¯¯¯JK=7. If ¯¯¯¯¯¯¯¯¯¯KN is perpendicular to ¯¯¯¯¯¯¯¯¯¯ML and if N is the midpoint of ¯¯¯¯¯¯¯¯¯¯ML, calculate the perimeter of JKLM.

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A
24.62
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B
23.25
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C
28
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D
31.596
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E
33.941
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Solution

The correct option is A 24.62
Given area of parallelogram JKLM is 28 and JK=7.KN is perpendicular to ML and N is the mid point of ML
NL=ML2=72=3.5
28=7×KN
KN=4
In triangle KNL
KL=(NL)2+(KN)2
=(3.5)2+(4)2
=16+12.25
=28.25
=5.31
Then perimeter of JKLM = 2(7+5.31)=24.62

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