Quadratic equations

[frankinaround]

Hi, I cant find a way to answer this question anywhere in this chapter but here it is :

the perimiter of a rectangle is 20 inches, and its area is 16 square inches. Find the dimensions of the rectangle.

I can guess, but I want to figure out how to actually do it. How do I set up the equation? (xy + 2xy -36=0 or something like that?)

 

[Mrspi]

Hi, I cant find a way to answer this question anywhere in this chapter but here it is :

the perimiter of a rectangle is 20 inches, and its area is 16 square inches. Find the dimensions of the rectangle.

I can guess, but I want to figure out how to actually do it. How do I set up the equation? (xy + 2xy -36=0 or something like that?)

START by defining variables to represent the unknowns.

You are asked to find the "dimensions of the rectangle"....so you want to find the width of the rectangle and the length of the rectangle.

Define variables:

let x = width of the rectangle
let y = length of the rectangle

The problem tells you that the perimeter of the rectangle is 20 inches. You know that, for a rectangle,

perimeter = length + width + length + width
20 = y + x + y + x
20 = 2y + 2x
Oh!!! You could divide both sides of that equation by 2!
20/2 = 2y/2 + 2x/2
10 = y + x

You also know that the AREA of the rectangle is 16 in^2. And you know that, for a rectangle,

area = length * width
16 = y * x
16 = xy

Ok...
you now have TWO equations in two variables:

10 = y + x
16 = xy

The ball is in your court now....show us where you might go from here to find x and y.

 

[frankinaround]

-x2+10x-16=0

Thanks!

I have 1 more question though :

The length of a rectangle is 4 inches more then the width. The area of the rectangle is 4 square inchs.
a. write an equation that can be used to find the length and width of the rectangle.
b.use the quadratic formula to find the length and width in radical form.
c.express the length and width to the nearest hundreth of an inch.

I got x*2 + 4x-4=0 for A, but I cant figure out how to factor it (because x(x+4)=4)

Where do I go from here?

 

[Denis]

I got x*2 + 4x-4=0 for A, but I cant figure out how to factor it (because x(x+4)=4)

Use the quadratic equation.

 

[frankinaround]

I dont understand, do you mean like graph it?

 

[Deleted member 4993]

For a quick refresher on quadratics - go to:

http://www.purplemath.com/modules/sqrquad.htm