+0  
 
0
67
1
avatar+101 

a)     The area of a rectangle is x^2+7x+13.  If the length is (x+4), write an expression for the width of the rectangle, including the remainder.

 

b)      If the perimeter of the rectangle is 7, what are the length and width? 

Whiz333  Jun 5, 2017

Best Answer 

 #1
avatar+4161 
+1

a)

area = length * width

x2 + 7x + 13  =  (x + 4) * width                 Divide both sides of the equation by (x + 4) .

(x2 + 7x + 13)/(x + 4)  =  width                 We can do this using long division....

 

 

So we get that

width  =  \(x+3+\frac1{x+4}\)

 

 

 

 

 

b)

perimeter = 2[ length  +  width ]

 

7 = 2[  x + 4  +  x + 3 + \(\frac1{x+4}\)  ]              Divide both sides by 2 .

 

3.5 = 2x + 7 + \(\frac1{x+4}\)                               Subtract 7 from both sides.

 

-3.5 = 2x + \(\frac1{x+4}\)                                    Multiply through by ( x + 4 )

 

-3.5(x + 4) = 2x(x + 4) + 1

 

-3.5x - 14 = 2x2 + 8x + 1                      Add  3.5x  and  14  to both sides.

 

0 = 2x2 + 11.5x + 15                             We can use the quadratic formula to solve for x.

 

\(x = {-11.5 \pm \sqrt{132.25-120} \over 4}={-11.5 \pm 3.5 \over 4}=-2.785\pm0.875\)

 

So, we get that  x = -2     and     x = -3.75

 

So......if x = -2

length = -2 + 4    =    2

width  = -2 + 3 + 1/(-2+4) = 1 + 1/2    =    1.5

 

And....if x = -3.75

length = -3.75 + 4    =    0.25

width  = -3.75 + 3 + 1/(-3.75+4) = -0.75 + 4    =    3.25

hectictar  Jun 5, 2017
Sort: 

1+0 Answers

 #1
avatar+4161 
+1
Best Answer

a)

area = length * width

x2 + 7x + 13  =  (x + 4) * width                 Divide both sides of the equation by (x + 4) .

(x2 + 7x + 13)/(x + 4)  =  width                 We can do this using long division....

 

 

So we get that

width  =  \(x+3+\frac1{x+4}\)

 

 

 

 

 

b)

perimeter = 2[ length  +  width ]

 

7 = 2[  x + 4  +  x + 3 + \(\frac1{x+4}\)  ]              Divide both sides by 2 .

 

3.5 = 2x + 7 + \(\frac1{x+4}\)                               Subtract 7 from both sides.

 

-3.5 = 2x + \(\frac1{x+4}\)                                    Multiply through by ( x + 4 )

 

-3.5(x + 4) = 2x(x + 4) + 1

 

-3.5x - 14 = 2x2 + 8x + 1                      Add  3.5x  and  14  to both sides.

 

0 = 2x2 + 11.5x + 15                             We can use the quadratic formula to solve for x.

 

\(x = {-11.5 \pm \sqrt{132.25-120} \over 4}={-11.5 \pm 3.5 \over 4}=-2.785\pm0.875\)

 

So, we get that  x = -2     and     x = -3.75

 

So......if x = -2

length = -2 + 4    =    2

width  = -2 + 3 + 1/(-2+4) = 1 + 1/2    =    1.5

 

And....if x = -3.75

length = -3.75 + 4    =    0.25

width  = -3.75 + 3 + 1/(-3.75+4) = -0.75 + 4    =    3.25

hectictar  Jun 5, 2017

7 Online Users

avatar
We use cookies to personalise content and ads, to provide social media features and to analyse our traffic. We also share information about your use of our site with our social media, advertising and analytics partners.  See details