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11 Dec 2008, 16:21
Kudos
Bookmarks
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
A. 56
B. 64
C. 68
D. 81
E. 100
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This topic has been closed and archived due to inactivity or violation of community quality standards. No more replies are possible here.
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11 Dec 2008, 17:48
Kudos
Bookmarks
haichao
Can you please check the q -
backworking will be easier and faster for this question -
Lets start with E
width of the patio is 10
width of the walkway is 5
width of the square including walkway is 15
width of the walkway is 15^2 - 10^2 = 125
Assuming that my assumptions are ok
12 Dec 2008, 15:04
Kudos
Bookmarks
My guess would be B = 64.
Let x be the width of the walkway. It is given that width of the pation is 5 greater than the width of the walkway. So patio width is x+5.
Area of the patio is (x+5) ^2.
Now the total length of the patio with walkway surrounded will be = length of the pation + 2 width of the patio (one on each side
= 3+5 +2x = 3x+5.
Area of the patio with Walkway suurended is (3x+5) ^ 2.
It is given that walk way area alone is 132.
So (3x + 5) ^ 2 - (x +5) ^2 = 132.
==> (4x+10)2x = 132 (applied (a+b)(a-b) = a^2 -b^2)
==> (2x+5)x = 33
==> x = 3
Length of the pation = x+ 5 = 8. Area is 8^2 = 64.
Let x be the width of the walkway. It is given that width of the pation is 5 greater than the width of the walkway. So patio width is x+5.
Area of the patio is (x+5) ^2.
Now the total length of the patio with walkway surrounded will be = length of the pation + 2 width of the patio (one on each side
= 3+5 +2x = 3x+5.
Area of the patio with Walkway suurended is (3x+5) ^ 2.
It is given that walk way area alone is 132.
So (3x + 5) ^ 2 - (x +5) ^2 = 132.
==> (4x+10)2x = 132 (applied (a+b)(a-b) = a^2 -b^2)
==> (2x+5)x = 33
==> x = 3
Length of the pation = x+ 5 = 8. Area is 8^2 = 64.
Archived Topic
Hi there,
This topic has been closed and archived due to inactivity or violation of community quality standards. No more replies are possible here.
Where to now? Join ongoing discussions on thousands of quality questions in our Quantitative Questions Forum
Still interested in this question? Check out the "Best Topics" block above for a better discussion on this exact question, as well as several more related questions.
Thank you for understanding, and happy exploring!
