SOLUTION: Please help me!!! The area of 10 cm by 25 cm rectangle is doubled by what equal amount must each dimension be increased? assignment for tomorrow. help me asap!!

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Question 902111: Please help me!!!
The area of 10 cm by 25 cm rectangle is doubled by what equal amount must each dimension be increased?
assignment for tomorrow. help me asap!!
Found 2 solutions by ewatrrr, Theo:
Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!
 

Hi,

     .

A = (10cm)(25cm) = 250cm^2

Question States***

A = (10cm + x)(25cm + x) = 500cm^2

x^2 + 35x - 500 = 0   (Tossing out the negative solution for unit measure)

 


 
Solved by pluggable solver: SOLVE quadratic equation with variable


Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B35x%2B-500+=+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=%2835%29%5E2-4%2A1%2A-500=3225.

  

  Discriminant d=3225 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-35%2B-sqrt%28+3225+%29%29%2F2%5Ca.

  

    x%5B1%5D+=+%28-%2835%29%2Bsqrt%28+3225+%29%29%2F2%5C1+=+10.8945417290014

    x%5B2%5D+=+%28-%2835%29-sqrt%28+3225+%29%29%2F2%5C1+=+-45.8945417290014

    

    Quadratic expression 1x%5E2%2B35x%2B-500 can be factored:

  1x%5E2%2B35x%2B-500+=+1%28x-10.8945417290014%29%2A%28x--45.8945417290014%29

  Again, the answer is: 10.8945417290014, -45.8945417290014.
Here's your graph:

graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B35%2Ax%2B-500+%29

Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
the area is increased by the square of the increase in the dimensions.

this means that, if the dimensions are increased by a factor of 2, then the area is increased by a factor of 2^2 = 4.

working backward, if the area is increased by a factor of 4, then the dimensions are increased by a factor of sqrt(4) = 2.

in your problem, the area was increased by a factor of 2.

using the rule shown above, this means that the dimensions must be increased by a factor of sqrt(2).

let's see if this rule holds.

your original area is 10 * 25 = 250 square units.

you multiply the area by a factor of 2 which means your new area is 500 square units.

you need to multiply your dimensions by a factor of sqrt(2) if the rule holds.

you will get:

10*sqrt(2)*25*sqrt(2) = 10*25*sqrt(2)*sqrt(2)= 10*25*2 = 500.

the rule works.

your solution is that each dimension must be multiplied by a factor of sqrt(2).