The area of a rectangular garden is 72 square meters. The width is 55 meters longer than ?one-third third of the length.

Question

Find the length and the width of the garden

Answer 1

Let x = length, so width = (1/3)x+55.

 

Area = 72 = x•[(1/3)x+55]

 

(1/3)x² + 55x = 72; clear fraction, multiplying all terms by 3 ⇒

x² + 165x -216 = 0.

 

Solving by quadratic formula: x = [-165 + √(165² -4(-216)] / 2

x = ½[167.6 - 165] = 1.30

 

So this value of x, 'length', is only 1.30 meters, so 'width' is 55.43 m; a very skinny rectangular garden.

 

There the answer, to the problem as stated. But I wonder if there might have been a decimal point lost, e.g. could the width have been 5.5 m longer than one third of the length?