Please help with this math problem

Question

Lazy can walk home from work by either of two routes. One takes her along two adjacent sides of a rectangular park who's length is 80 more than its width. The other route is a short cut along the diagonal of the rectangle. If the diagonal route is 100 m shorter than the other, what are the dimensions of the park?

Answer 1

d = L+w=100=w+80+w-100== 2w+80-100= 2w-20

d= 2w-20 = sqr(w^2+ (w+80)^2)

w^2 +w^2 +160w +6400 = 4w^2 -80w +400

2w^2 -240w -6000=0

w^2 -120w -3000 = 0

complete the square

w^2 -120w+60^2=3000+60^2

(w-60)^2 = 3000+ 3600=6600

w-60 = 10sqr66

w=60+10sqr66 = about 60+81.24 = 141.24 m wide

L=140+ 10sqr66 = about 221.24 m Long

d= 262.48 m diagonal