Question

KLMN is a rectangle with diagonals that intersect at point E. KE = 3x-3 and LN = 3x+5. Find LEA 7B 8C 15D) 16E 8.5

Answer 1

B. 8

Step-by-step explanation:

The diagram representing this problem is attached below:

In a rectangle, the diagonals are equal and bisect each other. Thus:

`\begin{gathered} KE=(1)/(2)LN \\ 3x-3=(1)/(2)(3x+5) \end{gathered}`

We solve for x:

`\begin{gathered} 2(3x-3)=3x+5 \\ 6x-6=3x+5 \\ 6x-3x=5+6 \\ 3x=11 \\ x=(11)/(3) \end{gathered}`

Therefore, the length of LE will be:

`\begin{gathered} LE=KE \\ LE=3x-3 \\ =3((11)/(3))-3 \\ =11-3 \\ =8\text{ units} \end{gathered}`

The length of LE is 8.