word problem help

Question

A square has a length and width of x. If the length of the square is increased by 2 units, and the width is increased by 3 units to create a larger rectangle. Find the perimeter of the rectangle in terms of x.

please explain as I am terrible with world problems relating to finding perimeter and area

Answer 1

It often helps to draw a picture, even though it is not to scale:

 

<   x   >|<  2  >|

* * * * * * * * *  -- 

*          *         *

*          *         *  X

*          *         *

* * * * * * * * *  --

*                     *

*                     *

*                     *  3

*                     *

*                     *

* * * * * * * * * --

 

The perimeter is the distance around the rectangle:

    (X+2) + (X+3) + (X+2) + (X+3)

    2L + 2W

     4X + 10

Answer 2

 

Perimeter = 2*Length + 2*width

 

 Length = x+2

 

Width = x+3

 

Perimeter = 2(x+2)+2(x+3) = 2x + 4 + 2x + 6 = 4x + 10 = 2(2x+5)

 

Now here's a quick check.

Let x=1.

THe length is 3 and hte width is 4. THe perimeter is 2*3+2*4 = 6+8 = 14

AND 2(2*1+5) = 2(2+5) = 2*7 = 14.

 

Of course, it should work with ANY value of x that you select.