Answer:
LM = 8 cm
Explanation:
LM = KN = x + 7
NM = KL = x + 7 + NQ = x + 7 + 2 = x + 9
KN×NM = 80
(x+7)(x+9) = 80
x² + 7x + 9x + 63 = 80
x² + 16x + 63 = 80
x² + 16x - 17 = 0
solution of a quadratic equation
x = (-b ± sqrt(b² - 4ac))/(2a)
a=1
b=16
c=-17
(-16 ± sqrt(256 + 4×17))/2 = (-16 ± sqrt(256+68))/2 =
= (-16 ± sqrt(324))/2 = (-16 ± 18)/2
x1 = (-16 + 18)/2 = 2/2 = 1
x2 = (-16 - 18)/2 = -34/2 = -17
x2 as negative value is no valid solution for a side length.
so, only x1 remand as solution.
=> x=1, LM = KN = 1+7 = 8, NM = KL = 1+9 = 10