If the distance from d to d' is 10 and the distance from a to d is 2, what is the scale factor

if the distance from d to d' is 10 and the distance from a to d is 2, what is the scale factor

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