Algebra/AREA

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Expert: Michael Tadesse - 9/25/2009


Question
A rectangular plot of ground having dimensions 40 feet by 36 feet is surrounded by a walk of uniform width. If the area of the walk is 492 ft 2  , what is its width?

Please enter your answer as a number without the units.
I have no idea how to set this up

Answer

Area
Hello Steven

I pictured the problem and you can see the image which will help you understand better.

As you can see in the image the area of the walk (green) is the area of the big rectangle minus the area of the red area. But we know the area of the red area

A = 36 * 40
A = 1440

So the Big rectangle is;

A – 1440 = 492 (the big minus the red area is the walk)

A = 1932 (the area of the big rectangle)

Now observe that the length of the length of the big rectangle is

L = 2D + 36

Also the width of the big rectangle is

W = 2D + 40

Remember D is the thickness or width of the walk we are trying to find.

A = 1932, area of the big rectangle.

1932 = L * W
1932 = (2D + 36) * (2D + 40) multiply them and collect like terms.
1932 = 4D2 + 152D + 1440
1932 – 1440 = 4D2 + 152D
492 = 4D2 + 152D
0 = 4D2 + 152D – 492

Steve, you can use the quadratic formula to find D

Recall the quadratic formula operate

D = 3

Therefore, the thickness of the walk is 3 units wide.

Michael Tadesse

Expertise

I can answer questions regarding Relations, linear functions and equations, Squares and square roots, Translation and Similarity, Special Properties of Right Angled Triangles, Measurement of Area and Volume, algebra. I can also answer questions related to Pre calculus, Limits and Continuity, Derivatives Applications of Derivatives, High school math in general. I can’t answer questions of the following type. Power Series, Multiple Integrals, Fourier series, Vector valued Functions.

Experience

I love mathematics as it is the mother of all sciences. I had an outstanding math results while I was in school. The tradition continues while I am in university. I have been helping elementary school Students for the past five years with mathematics problems. In fact, I have a brother who is four years younger than me I usually help him to understand what the crux of the question is before trying to solve it. He loves math very much, he is indeed one of the top scorers form his class in Mathematics. I didn’t stop helping my younger relatives after I joined the Engineering campus and I am more than ready to help anyone with my skill.

Education/Credentials
have a high school diploma with a 3.97 GPA; I also have many merit certificates granted for my outstanding results in high school math. I won a merit certificate for my participation in the Black Month Essay Contest. I took two different National Examinations in 2006 and 2007. In the former Exam I got 9As which includes Mathematics. I also have a score of 90 out of hundred in the later Examination which is the toughest known in Ethiopia. So you don’t have to worry about my ability to help my clients.

Past/Present Clients
I have never had an online client but I was helping students coming to me for assistance in Mathematics.

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