Answer:
10.6 feet
Step-by-step explanation:
Length = 22ft
width= 14ft
Maximum area = 800 sq. ft
Let X be increase in the number of feet for the length and width.
The new length = (22 + x) ft
New width= (14 + x) ft
Area = (22+x)(14+x) ≤ 800
308 + 36x + x^2 ≤ 800
x^2 + 36x + 308 - 800 ≤ 0
x^2 + 36x - 492 ≤ 0
Solve using quadratic equation
x = (-b +/- √b^2 - 4ac) / 2a
a= 1, b = 36, c= 492
x = (-36 +/- √36^2 - 4*1*-492)/ 2*1
= (-36 +/- √1396 + 1968) / 2
= (-36 +/- √3264) / 2
= (-36 +/- 57.13) / 2
x = (-36 + 57.13)/2 or (-36 - 57.13)/2
x = 21.13/2 or -93.13/2
x = 10.6 or -31.0
x = 10.6 ft
The length and width must increase by 10.6 ft each
