Answer:
Length = width + 32, where width > 5.36
Explanation:
Let,
width of the floor be = x
length of the floor = x + 32
area of the floor > 200 m²
From the statement of the problem;
x(x + 32) > 200
x² + 32x - 200 > 0
Solving the quadratic by formula method;
x = (-b +√ b² - 4ac) / 2a
Note;
a = 1
b= 32
c= -200
x = -32 ±√32² - (4 • 1 • (-200)) / (2) (1)
x = -32 ±√1024 + 800) / 2
x =-32 ±42.71/2
So the roots are,
x1 = - 37.4
x2 = 5.36
But length can not be negative hence; x = 5.36
Substituting values;
width = 5.36
length = 5.36 + 32 = 37.36
