the perimeter of a rectangular ranch is 18 miles and the area is 20 square miles. find the dimensions

Question

word problems using quadratic equations

Answer 1

A*B = Area= 20

2A + 2B = 18

A= 20/B, replacing in equation 2

40/B + 2B = 18B

2B^2 -18B +40 = 0

solving the quadratic we obtain B1 = 5 miles; B2 4 Miles. Then also replacing in equation 1 we get: A1 = 4 Miles and A2= 5 miles.

Answer is Length 5 miles width 4 miles. or Length 4 miles and width 5 miles.