Area

Answer : B (64)

Width of the patio = x+5

Width of the walkway = 3x+5

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

solving this equation will give x = 3

So, the side of the patio = 8 and the area of the patio = 64.

What is the OA ?

how did you get the width of the walkway?

yvichman wrote:how did you get the width of the walkway?

From the figure, the distance between patio wall and outer wall of walkway is x, width of patio is defined as being 5 more than this width = x+5

Each side of walkway = x + (x+5) + x = 3x + 5

OA should be 64

Area of walkways = area of bigger sq - area os smaller sq
= (3x+5) ^2 - (x+5) ^ 2 = 132

x = 3

thus area of patio = samll sq = 8^ 2 = 64

Side of patio = a
Side of walkway = x
=> x = a-5.

Area of walkway = Total area of square(including walkway) - area of patio

132 = (x+a+x)^2 - a^2
132 = (a+2x)^2 - a^2

Replace the value of x=a-5 =>
132 = (31-10)^2-a^2

By solving this you will get a^2=64. Answer = B

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

solving this equation will give x = 3

can someone solve the above equation pls? Tx.

Quote:
Area of Walkway = (3x+5) ^2 - (x+5)^2 = 132

solving this equation will give x = 3


can someone solve the above equation pls? Tx.

9x^2+30x+25-x^2-10x-25=132

8x^2+20x-132=0

Quadratic formula:

-20+/-sqrt(400-4(8)(-132))/16=-20+/- 68/16=68-20/16=48/16=3.

Disregard the negative number you get from the formula.

How are you calulating the sq rt of 4624?

any short cuts besides factoring?

How are you calulating the sq rt of 4624?

any short cuts besides factoring?

It really isn't that difficult to take the square root of 4624. You know that 60^2=3600 and 70^2= 4900, so the square root of 4624 must be somewhere around 60 and 70. What two numbers between 60 and 70 have a units digit of 4 when squared? 62 and 68. 62 can't be the square root of 4624 since it's more close to 60, only 68 makes sense.

gotcha, thanks. That was the info i was looking for.

Disregard the negative number you get from the formula.

I am guessing the reason for the above is coz x cannot be a negative number..correct?

Tx much for solving.

One additional note

Once you get down to 8x^2 +20x-132=0, you can divide this by 4 instead of using the quadratic formula. (2 minutes per question on the actual GMAT really doesn't allow you enough time to use the quadratic)

This comes out to:
2x^2+ 5x-33=0
(2x+11) (x-3) =0
since x cannot equal -11/2, x=3

anjaligeorge1 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

If we let x = the width of the walkway, then the width of the patio = x + 5. Let’s create the equation for the area of the combined walkway and patio. We see that the entire length of the combined walkway-patio is (x + x + x + 5) = (3x + 5). Because it is a square, we square (3x + 5) to determine the combined area. We see that this is equal to the area of the patio plus the area of the walkway:

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

9x^3 + 30x + 25 = x^2 + 10x + 25 + 132

8x^2 + 20x - 132 = 0

2x^2 + 5x - 33 = 0

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

2x + 11 = 0

2x = -11

x = -5.5

Or x = 3

Since x cannot be negative, x = 3.

Since x = 3, the area of the patio is (3 + 5)^2 = 8^2 = 64.

Answer: B