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Expert: Robi Bhattacharjee - 3/8/2009


Question
i have no problems with using the quadratic formula, but i just couldn't equate this problem right...please help me!!!

here it is:

"a mural is to be painted on a wall that is 15m long and 12m high. a border of uniform width is to surround the mural. if the mural is to cover 75% of the area of the wall, how wide must the border be, to the nearest hundredth of a meter?"

the answer at the back of my book is 0.89m.

i really hope you can help me!! hopefully, before march 11 because my assignment is due on the 12th. thanks so much and take care!!!!

Answer
Hello,

Well, suppose that the width of the border is x.

Then, the dimensions of your mural will be (15 - 2x) by (12 - 2x). The reason for the 2x is since you have to subtract from both the top and the bottom. This is since your border goes all around the mural.

So, the area of the mural is (15 - 2x)(12 - 2x).

Now since it equals 75% of the total area which is 15*12, we have

(15 - 2x)(12 - 2x) = 15*12*0.75

or 180 - 24x - 30x +4x^2 = 135

or 4x^2 - 54x + 45 = 0

so applying the quadratic formula

x = (54 (+ or -) sqrt(54^2 - 4*4*45))/8 = .89 m

The other solution was too big to fit on the wall of the mural.


Feel Free to ask again,
Robi

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Robi Bhattacharjee

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I can answer a variety of questions on mathematics. Questions on trigonometry, calculus(preferably single variable), algebra, geometry, and number theory will be answered. I cannot answer questions on abstract branches of mathematics such as group theory. I also cannot answer questions on statistics. In number theory, I can answer questions on congruences, prime numbers, units, functions, and the riemann-zeta function.

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I have studied advanced math my entire life. I started calculus in sixth grade. I have attended numerous math competitions and I am attending math organizations such as the San-Diego math circle. Also, this year I have been invited to the USAMO which is a prestigious math competition (Every year the USAMO invites 500 students from across the USA to participate in this competition. The top 6 go to represent the USA in the International Math Olympiad).

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I am in the San Diego Math Circle

Education/Credentials
I am entering high school and have received a perfect score and the STAR test 5 times in a row. I also have gotten recognitions in the AMC 10, AIME, Math Counts, and ARML. Additionally, I have won the San Diego Math Olimpiad twice in a row.

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