Answer:
....A rectangle has an area of 96 cm? and a perimeter of 44 cm. What is the length and width?
x= length
y = width
2(x+y)= 44
the half perimeter = x+y=22cm
area = xy=96cm²
we have a :
x+y=22
xy=96
we substitute y in x+y=22→y=(22-x)
we replace y in xy=96→x(22-x)=96→22x-x²-96=0
we have the equation -x²+22x-96=0
b²-4ac = 22²-4(-1*-96)=100
delta =100
Δ is strictly positive, the equation −x²+22x−96=0 admits two solutions.
(-b-√Δ)/2a= (-22-10)/-2 = 16
(-b+√Δ)/2=(-22+10)/-2=6
solution x1=16, x2=6
length = 16cm, width = 6cm