Given that the pentagons ABCDE and JKLMN.
Let's find the length of KL.
Given:
AB = 3
BC = 2
CD = 4
DE = 3
AE = 5
KJ = 2.1
KL = x
LM = 2.8
MN = 2.1
JN = 3.5
Since the pentagons are similar, then the corresponding sides are in proportion.
Thus, we have:
[tex]\frac{AB}{KJ}=\frac{BC}{KL}=\frac{CD}{LM}=\frac{DE}{MN}=\frac{AE}{JN}[/tex]
To find the value of KL, apply the proportionality equation.
We have:
[tex]\frac{AB}{KJ}=\frac{BC}{KL}[/tex]
Input values into the equation:
[tex]\frac{3}{2.1}=\frac{2}{x}[/tex]
Let's solve for x.
Cross multiply:
[tex]\begin{gathered} 3x=2\times2.1 \\ \\ 3x=4.2 \end{gathered}[/tex]
Divide both sides by 3:
[tex]\begin{gathered} \frac{3x}{3}=\frac{4.2}{3} \\ \\ x=1.4 \end{gathered}[/tex]
Therefore, the value length of KL is 1.4 units.
ANSWER:
x = 1.4
