# 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

 Ad: Mathway solves algebra homework problems with step-by-step help! Ad: Algebrator™ solves your algebra problems and provides step-by-step explanations!

 Geometry: Rectangles Solvers Lessons Answers archive Quiz In Depth

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?

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 (in our case ) has the following solutons: For these solutions to exist, the discriminant should not be a negative number. First, we need to compute the discriminant : . Discriminant d=36 is greater than zero. That means that there are two solutions: . Quadratic expression can be factored: Again, the answer is: 16, 10. Here's your graph: