amitdgr wrote:

The figure shows a square patio surrounded by a walkway of width x meters. If the area of the walkway is 132 square meters and the width of the patio is 5 meters greater than the width of the walkway, what is the area of the patio, in square meters?

A. 56

B. 64

C. 68

D. 81

E. 100

Smaller square=Patio

Let the side of Patio be "s".

Width of walkway=x

width of the patio is 5 meters greater than the width of the walkway(Actually it should be "side of the patio is 5 meters greater than the width of the walkway" because patio is a square)

So,

\(s=x+5\)

If we see the figure properly, the outer quadrilateral is also a square with side \(s+x+x\) OR \(x+5+x+x=3x+5\)

We know, the area of the walkway is 132 square meters:

Area of walkway=Area of outer square-Area of inner square

Area of walkway=(3x+5)^2-(x+5)^2=132

\((3x+5)^2-(x+5)^2=132\)

\((3x)^2+(5)^2+2*3x*5-(x^2+5^2+2*5x)=132\)

\(9x^2+25+30x-x^2-25-10x=132\)

\(9x^2+30x-x^2-10x=132\)

\(8x^2+20x=132\)

\(2x^2+5x=33\)

\(2x^2+5x-33=0\)

\(2x^2+11x-6x-33=0\)

\(x(2x+11)-3(2x+11)=0\)

\((x-3)(2x+11)=0\)

\(x=3 \hspace{3} OR \hspace{3} x=-\frac{11}{2}\)

Width can't be -ve. So, \(x=3\)

\(s=x+5=3+5=8\)

Area of the patio\(=s^2=8^2=64\)

Ans: "B"

_________________

~fluke

GMAT Club Premium Membership - big benefits and savings