SOLUTION: Lady Greenthumb has a rectangular garden that measures 12m by 5m. Since it is still possible for her to extend her garden, she cultivated a uniform width of land around the garden,
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Question 698534: Lady Greenthumb has a rectangular garden that measures 12m by 5m. Since it is still possible for her to extend her garden, she cultivated a uniform width of land around the garden, thereby doubling the area. Find the dimensions of the new garden. Answer by Simnepi(216) (Show Source):
You can put this solution on YOUR website! putting a border around the garden increases each dimension by twice the width of the border. (Draw a sketch!)
Let the width of this border be called x.
The new dimensions of the garden are 12+2x and 5+2x.
The area is doubled (The original area is 12m X 5m = 60m^2) so we can write an equation to find the new area thus..
(12+2x)(5+2x) = 120
Expanding the bracket and simplifying gives
60 + 34x + 4x^2 = 120
divide by 2 throughout (to make the numbers smaller) giving
30 + 17x + 2x^2 = 60
rearranging this we get
2x^2 + 17x - 30 = 0
Now we have to factorize
Find factors of -30 (the constant term) i.e. (plus/minus) 2 and 15, 3 and 10, 5 and 6
We also have to consider the coefficient of the x^2 term (which is 2!)
now we try to make +17 (the coefficient of the x term) using the factor pairs and the 2 from the x^2 term
By trial and error we find that 2 X 10 and -3 can make +17. thus we get
(2x-3)(x+10) = 0
thus either (x+10) = 0 or (2x-3) = 0
if (x=10)=0 then x = -10 (a negative measurement is nonsense)
so (2x-3)=0
therefore 2x = 3
so x = m (1.5m)
