A large city in the ancient world was square-shaped. Measured in miles, its area numerically exceeded its perimeter by about 121. Find its dimensions. (Round to

Question

A large city in the ancient world was square-shaped. Measured in miles, its area numerically exceeded its perimeter by about 121. Find its dimensions. (Round to the nearest tenth.)

 

Larger value-

Smaller value-

Answer 1

s^2=4s+121

s^2-4s-121=0

(-b±√(b^2-4ac))/2a

(4±√16+484))/2

(4±√500)/2

(4±10√5)/2

2±5√5

2+5√5

check:(2+5√5)^2=4(2+5√5)+121

          4+20√5+125=8+20√5+121

         129+20√5=129+20√5

the square is 2+5√5 miles or 2+11.18=13.18 miles

13.18 rounded to the nearest tenth is 13.2 miles