Given: lmnk is a rhombus km + ln = 7 area of klmn = 6. find: kl

We know that
The area of a rhombus is half the product of the diagonals
so
A=(1/2)*[KM*LN]
A=6 units²
6=(1/2)*[KM*LN]-----> 12=KM*LN-----> KM=12/LN-----> equation 1
KM+LN=7-----> equation 2

substitute equation 1 in equation 2
[12/LN]+LN=7------> multiply by LN both sides----> 12+LN²=7LN
LN²-7LN+12=0

using a graph tool
see the attached figure
LN=3
KM=4

find KL
applying the Pythagoras Theorem
KL²=(LN/2)²+(KM/2)²-----> (3/2)²+(4/2)²----> 25/4
KL=5/2-----> KL=2.5 units

the answer is
KL=2.5 units