Find the lenght and the width of the batters box

Question

The lenght of the batters box on a softball field is 1ft more than the width. The area of the batters box is 21ft^2. Find the lenght and width of the rectangular batters box.

Answer 1

x(x+1) = 21

x(x+1)-21 = 0

x^2 + x - 21 = 0

x = [-1 + sqrt( 1 + 84)] / 2

= [ sqrt(85) - 1]/2

width is [sqrt(85)-1]/2

length is [sqrt(85) + 1]/2

area is [sqrt(85) - 1][ sqrt(85) + 1]/4

= [85 - 1]/4

= 84/4

= 21

so the answers in bold are correct