a rectangul is 50m long and 34m wide;surrounded by a uniform dirt road. find the width of the road if the total area of the garden and road is 540 m^2

Question

a rectangular garden 50 m long and 34 m wide is surrounded by a uniform dirt road. find the width of the road if the total area of the garden and road is 540 m^2

Answer 1

50 m long, 34 m wide Area = 50(34) = 1700 m^2 for the rectangular garden alone

You probably left off a zero on the "540"

Area of garden & road =5400 m^2 = (50+2x)(34+2x) = 1700+168x +4x^2

4x^2 + 168x -3700 = 0

x^2 + 42x - 925 = 0

either factor, complete the square or use the quadratic formula. Doesn't see to factor so try completing the square

take half of the x coefficient, 42/2 = 21, square it and add it to both sides

x^2 +42x + 441 = 925 + 441

(x+21)^2 = 1366

x +21 = sqr1366

x =-21 +about 37 = 16 m wide road (ignore the negative square root)