The figure shows a square patio surrounded by a walkway of width x

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

Solving for x = 64

Hence B

I eventually didn't understand the figure . The outer box is the walkway and the inner one is the patio. Am i correct? Sorry seems like silly question, but iam weak in geometry and it would really great if someone could help me understand the figure.

We are given that the patio is surrounded by a walkway, so yellow area is walkway and red is patio itself.

Thank youBunuel

I did not realise this when I first read the question but with hindsight the fastest way to solve this is to realise that:

both the answer and answer+132 must be perfect squares so:

A) 56 not a square
B) 64 is ok and 64+132 =196 is also ok
C) 58 not a square
D) 81+132 = 213 not a square
E) 100+132 = 232 not a square

so answer is C

Leave everything else.
If I have to add something to 132 the result should be a perfect square. Option B works.

Since it is a square the area should be a perfect square.

Area given 132

Option b 64

Total area 64+132=196

Side =14

Only this option has a perfect square

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Ans 64. Attached solution

Posted from my mobile device

132+64 = 196
ONLY AVAILABLE CHOICE WHEN ADDED TO 132 GIVES PERFECT SQUARE
ANS:B

We can PLUG IN THE ANSWERS, which represent the area of the patio.
Since the area of the walkway = 132, the correct answer must yield the following:
outer square - patio = 132

D: 81
Since the area of the patio = 81, each side of the patio = 9 meters
Since the width of the walkway is 5 less than the width of the patio, the width of the walkway = 9-5 = 4 meters
Since the walkway extends 4 meters to the left of the patio and another 4 meters to the right of the patio, the width of the outer square = 4+9+4 = 17, implying that the area of the outer square \(= 17^2 = 289\)
Resulting difference:
outer square - patio = 289-81 = 208
The difference is too great.
Eliminate D.

B: 64
Since the area of the patio = 64, each side of the patio = 8 meters
Since the width of the walkway is 5 less than the width of the patio, the width of the walkway = 8-5 = 3 meters
Since the walkway extends 3 meters to the left of the patio and another 3 meters to the right of the patio, the width of the outer square = 3+8+3 = 14, implying that the area of the outer square \(= 14^2 = 196\)
Resulting difference:
outer square - patio =196-64 = 132
Success!

[quote="LiveStronger"]B

(5+3x)^2 - (5+x)^2 = 132
2x(10+4x) = 132
x(5+2x) = 33 = 3*11
So, x can be 3 and not 11

8^2 = 64[/q

how is the side of the large cube is 5?

Area of Walkway = (Area of Entire Square) - (Area of Inner Patio Square)

Side Length of Inner Square Patio ------> the width/side is +5 more than the width X of the patio -----> A = (X + 5)

Side Length of ENTIRE Square ------> (X + 5) + X + X = (3X + 5)


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

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

8X^2 + 20X = 132

2X^2 + 5X = 33

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

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

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

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

Since the Width = X can NOT be (-)Negative, the Width X must = +3

Area of Patio is given by ----> (X + 5)^2 = (3 + 5)^2 =

64

-B-

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