Question

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

• A. 24.62
• B. 23.25
• C. 28
• D. 31.596
• E. 33.941

Answer 1

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 $ML$

$NL=\frac{ML}{2}=\frac{7}{2}=3.5$

$\therefore 28=7\times KN$

$\therefore KN=4$

In triangle $KNL$

$KL=\sqrt{(NL{)}^2+(KN{)}^2}$

$=\sqrt{(3.5{)}^2+(4{)}^2}$

$=\sqrt{16+12.25}$

$=\sqrt{28.25}$

$=5.31$

Then perimeter of $JKLM$ $=$ $2(7+5.31)=24.62$