SOLUTION: A rectangular garden measures 8m by 14m. we want to double the area of the garden by adding equal lengths to both dimension. Determine this length to the nearest tenth of a metre.

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Question 833965: A rectangular garden measures 8m by 14m. we want to double the area of the garden by adding equal lengths to both dimension. Determine this length to the nearest tenth of a metre.
Answer by DrBeeee(684) About Me  (Show Source):
You can put this solution on YOUR website!
Given:
l = 14
w = 8 then
a = 14*8 = 112
We want to add x meters to l and w to double the area, or
(1) (14+x)*(8+x) = 2*112 or
(2) 112 + 14x + 8x + x^2 = 224 or
(3) x^2 + 22x - 112 = 0
Use the quadratic solution equation
(4) %28-b%2B-sqrt%28b%5E2-4%2Aa%2Ac%29%29%2F%282%2Aa%29 to get
(5) %28-22%2B-sqrt%2822%5E2-4%2A1%2A%28-112%29%29%29%2F%282%2A1%29 or
(6) x = -26.264, 4.264
Using the positive value of x for the number of meters to add to the original rectangular dimensions to get
(7) A = (14+4.264)*(8+4.264) or
(8) A = 223.996
Answer: Add 4.3 meters (nearest tenth) to each of the rectangular dimensions.