Answer:
[tex]LE=5\ units[/tex]
Step-by-step explanation:
we know that
In a rectangle, the two diagonals are congruent and each diagonal bisects the other
so
[tex]LN=2KE[/tex] ----> equation A
[tex]KE=LE[/tex] -----> equation B
step 1
Find the value of x
solve equation A
[tex]LN=2KE[/tex]
substitute the given values
[tex](2x+2)=2(3x-7)[/tex]
solve for x
[tex]2x+2=6x-14\\6x-2x=2+14\\4x=16\\x=4[/tex]
step 2
Find the value of KE
[tex]KE=3x-7[/tex]
substitute the value of x
[tex]KE=3(4)-7=5\ units[/tex]
Remember that
[tex]KE=LE[/tex] -----> by each diagonal bisects the other
therefore
[tex]LE=5\ units[/tex]
