longer side?

grandh01 wrote:If the perimeter of a rectangular garden
plot is 34 feet and its area is 60 square
feet, what is the length of each of the
longer sides?
(A) 5ft
(B) 6ft
(C) 10ft
(D) 12ft
(E) 15ft

Perimeter = 2 (a+b) = 34 --> a+b = 17
a = 17 - b [eq1]

Area = ab = 60
(17-b)b = 60
b^2 - 17b + 60 = 0
b^2 - 12b - 5b + 60 = 0
b(b - 12) + 5(b - 12)
(b - 5) (b - 12) = 0
b = 5 or 12

using eq1,
if b = 5, a =12
if b = 12, a = 5

the longer side is always going to be 12
ans = d

grandh01 wrote:If the perimeter of a rectangular garden
plot is 34 feet and its area is 60 square
feet, what is the length of each of the
longer sides?
(A) 5ft
(B) 6ft
(C) 10ft
(D) 12ft
(E) 15ft

To solve this problem it's important to understand the equations of perimeter and area of a rectangle and their relationship together. This is a fairly common GMAT question type.

Perimeter= 2l+2w (where w=width, l= length)
Area= wl (where w and l mean the same as above)

We are given both the Perimeter and the Area. That is two equations with two variables so we can solve this problem (it's important to know that for DS questions). We have to solve it here and we are going to be a quadratic equations.

2l+2w = 34 (the Perimeter)lets solve for one variable
l+w = 17 (I factored out a 2 and divided by 2 by both sides)
l=17-w (solved for l)

lw=60 (the Area) lets plug in l from the equation above

(17-w)(w) = 60
17w-w^2 = 60
-w^2 + 17 - 60 = 0 (solve for 0 so we can solve the quadratic)
w^2 - 17 + 60 = 0 (multiply both sides by -1 so we don't deal with a -w^2)
(now think what multiples to get a 60 and adds to get a -17)
(w-5)(w-12) = 0
so... w=5 and w=12.

Here we have two solutions, and we should (there are two different sides of a rectangle!). The question asks for the longer side and clearly 12 is longer than 5. So the correct answer is 12 answer choice D

Hope this helps