SOLUTION: A rectangular gardon measures 5m by 7m. Both dimensions are to be extended by the same amount so that the areaof the gardon is doubled. By how much should the dimensions increases,

Algebra ->  Pythagorean-theorem -> SOLUTION: A rectangular gardon measures 5m by 7m. Both dimensions are to be extended by the same amount so that the areaof the gardon is doubled. By how much should the dimensions increases,      Log On


   

Question 312346: A rectangular gardon measures 5m by 7m. Both dimensions are to be extended by the same amount so that the areaof the gardon is doubled. By how much should the dimensions increases, to the nearest tenth of a metre.
Answer by mollukutti(30) About Me  (Show Source):
You can put this solution on YOUR website!
The length of the garden=7m
Width = 5m
Area = 7 x 5 = 35 sq m
Let us increase the dimensions by x m
Area = (7+x)(5+x)
As per given condition
(7+x)(5+x) = 2 x 35
or, 35 + 7x + 5x + x^2 =70
or, x^2 + 12x + 35 - 70 =0
or, x^2 + 12x - 35 =0
Here we need to consider the positive value of x which will come to 2.4 m approx as per the solver given below
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B12x%2B-35+=+0) has the following solutons:

x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca

For these solutions to exist, the discriminant b%5E2-4ac should not be a negative number.

First, we need to compute the discriminant b%5E2-4ac: b%5E2-4ac=%2812%29%5E2-4%2A1%2A-35=284.

Discriminant d=284 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-12%2B-sqrt%28+284+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%2812%29%2Bsqrt%28+284+%29%29%2F2%5C1+=+2.42614977317636
x%5B2%5D+=+%28-%2812%29-sqrt%28+284+%29%29%2F2%5C1+=+-14.4261497731764

Quadratic expression 1x%5E2%2B12x%2B-35 can be factored:
1x%5E2%2B12x%2B-35+=+1%28x-2.42614977317636%29%2A%28x--14.4261497731764%29
Again, the answer is: 2.42614977317636, -14.4261497731764. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B12%2Ax%2B-35+%29