SOLUTION: I have 2 questions: 1.) Factor the expression: x2 - 4x + 4 2.) The perimeter of a rectangle is 52 cm. Its area is 160 cm2. What are the dimensions of the rectangle? Please

Algebra ->  Rectangles -> SOLUTION: I have 2 questions: 1.) Factor the expression: x2 - 4x + 4 2.) The perimeter of a rectangle is 52 cm. Its area is 160 cm2. What are the dimensions of the rectangle? Please      Log On


   

Question 435414: I have 2 questions:
1.) Factor the expression: x2 - 4x + 4
2.) The perimeter of a rectangle is 52 cm. Its area is 160 cm2. What are the dimensions of the rectangle?
Please and thank you.
Answer by jorel1380(3719) About Me  (Show Source):
You can put this solution on YOUR website!
1.)x2-4x+4=(x-2)(x-2)=(x-2)2
2.)p=2L+2W
52=2L+2W
26=L+W
26-W=L
---------------
LXW=160
(26-W)W=160
26W-W2=160
0=W2-26W+160
0=(W-16)(W-10)
The width is 10cm. The length is 16cm.
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B-26x%2B160+=+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=%28-26%29%5E2-4%2A1%2A160=36.

Discriminant d=36 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--26%2B-sqrt%28+36+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-26%29%2Bsqrt%28+36+%29%29%2F2%5C1+=+16
x%5B2%5D+=+%28-%28-26%29-sqrt%28+36+%29%29%2F2%5C1+=+10

Quadratic expression 1x%5E2%2B-26x%2B160 can be factored:
1x%5E2%2B-26x%2B160+=+1%28x-16%29%2A%28x-10%29
Again, the answer is: 16, 10. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B-26%2Ax%2B160+%29