A rectangular public park has an area of 3,600 square feet. It is surrounded on three sides by a chain link fence. If the entire length of the fence measures 180 feet, how many feet long could the unfenced side of the rectangular park be?

A. 30

B. 40

C. 60

D. 90

E. 120

Why can’t 30 be an answer(multiple answer choice), as 30*120=3600 and 30+120+30=180 so it completes the requirements as shown on Dedicated Quant Strategies Session 3 35 minute’s problem.

Others 60\times60=3600 and 60+60+60=180 also works and verified as answers in the book but 30 is not shown as an answer, though if solved algebrically 30 crosses out but what am I missing here?

Thank you.

Thank you but I have understood the algebric approach, I am actually looking for backsolve method shown in ‘Dedicated Quant Strategies Session 3’ 35 minute’s problem. It would be very helpful if can provide solution related to that, thanks.

If you wanna use backsolve , then all answer choices are the length (L) and we are given that L+2W(fenced) = 180, thus \frac{180-L\text{(from options)}}{2} will give us the width of rectangle .Also, we are given the area of rectangle which equals to 3600 (\text{L}\times\text{W})

For eg : if we choose L = 30(option A ) then, the width of rectangle \frac{180-30\text{(from options)}}{2} or 75(this is the width) but this ain’t the answer. We need to also check if L x W is equal to 3600.

Hence, 75 x 30 = 2250(Which does not equal 3600). Thus, option A is wrong.