Answer:
...x= width
x+5 = length
A = 24 cm²
x(x+5)=24
x²+5x-24=0
Δ = b²-4ac = 5²-4(1*-24)= 121
Δ is strictly positive, the equation x²+5x−24=0 admits two solutions
(-b-√Δ)/2a =(-5-11)/2= -8
(-b+√Δ)/2a=(-5+11)/2 = 3
a length is never negative, we keep the positive value, i.e. 3
x=3
x= width = 3cm
x+5 = length = 3+5 =8cm