Please refer to the details section for this math question that I need help with.?

I have the answer but need to be able to show work for it



Question:



Juan, a landscaper in Alburquerque, designing a spring display of tulips and daffodils. The city has requested a 6-ft by 8-ft area of tulips surrounded by a uniform border of daffodils. The total area of tulips are daffodils is to be 100 ft^2. How wide should the border be?



Answer: -7+(SquareRoot of 101)/2 = 1.52 FT

Please refer to the details section for this math question that I need help with.?
There is a rectangle, 6x8 inside of a larger rectangle. The distance between the inner and outer is "x", and we're assuming it's uniform all the way around.



So the 6ft side of the rectangle has x on the left and x on the right, so the total side is 6 + 2x. The 8ft side has x on top and x on bottom, or 8 + 2x total.



Area is length * width, and you know total area, border and all, is 100.



100 = (6+2x)(8+2x)



100 = 48 + 28x + 4x^2 %26lt;--- you can divide through by 4 here



25 = 12 + 7x + x^2; make the equation = 0 by subtracting 25 from both sides, and reorder a bit:



0 = x^2 + 7x - 13



Now use quadratic formula to solve for x; when ax^2 + bx + c = 0; x = [-b +/- sqrt(b^2 - 4ac)]/2a



so for x^2 + 7x - 13 = 0 a is 1; b is 7; and c is -13



x = [-7 +/- sqrt(7^2 - (4)(1)(-13)]/2*1



= [-7 +/- sqrt(49 + 52)]/2



= [-7 +/- sqrt(101)]/2 %26lt;-- you would only consider the plus, since -7 minus sqrt101 would give you a negative number, thus your answer



x = [-7 + sqrt(101)]/2 = approx. 1.52 ft
Reply:First draw a picture if you don't already have one. There's an 8x6 inner rectangle and an outer rectangle. The outer is separated from the inner by the unknown border width, call it X/2. Then how long are the sides of the outer rectangle? 8+X and 6+X, right? And the product of those two sides is the area. This gives you a quadratic equation which you solve for X.
Reply:just write down first part, get work, and work onto the pronblem

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