Problem Solving

I ran across the problem below and had some trouble with it. I know i can solve it, but it involves tons of multiplication and hte use of the quadratic formula...Is there a quicker way (without resorting to back solving) ?

A rectangular yard is 20 yards wide and 40 yards long. It is surrounded by a thick hedge that grows on the boarder of the property, but comkpletely within the boundaries of the yard. If the hedge covers and area of 171yards^2, what is the width?

a. 160/120
b. 171/120
c. 180/120
d. 191/120
e. 800/120

(thanks!)

Well, I got this equation:

171 = 120x - 4x^2

x being the width of the hedge.

This tells me that it can't be (A) or (B), because x > 171/120 in order to be able to subtract that 4x^2 and still equal 171. (E) seems absurd to me, so if I encountered this question, I'd be at a 50/50 guess between C & D.

I think at this point I'd backsolve. I'll try (C) since it's much cleaner. The nice thing is that the 120 term would cancel out, so you'd be left with

171 = 180 - 4*(180/120)^2

3/2^2 --> 9/4 * 4 --> 36/4 --> 9. 180 - 9 = 171.

(C) is our answer. If this had not been the correct answer, then I would've gone with (D) by elimination.

BTW: Backsolving would've been an excellent strategy here. You would've gotten the correct answer right away (i.e. C) once you got the quadratic equation.

Well, I got this equation:

171 = 120x - 4x^2

Can you explain how you did you get the quadratic? Tx

Even I have a doubt as to how u got
171=120x-4x^2

Shouldnt it be 171=120x+4x^2?

Area of the hedge = (20+2x)(40+2x) - 40*20
=120x+4x^2 = 171

Can u please clarify?

sanjana wrote: Shouldnt it be 171=120x+4x^2?

Sanjana,

I guess 171=120x-4x^2 is right. See the words "hedge completely within boundaries of the field"

So it will be (40-2x)(20-2x).. not (40+2x)(20+2x)

Hope my reason is meaningful!