Thread: Rectangle problem-probably easy

Suppose the length of a rectangle is twice the width. If we increase both the width and length of the rectangle by 2 units, the area is increased by 34 square units. Find the width of the rectangle.

Can someone explain the process of finding the answer?
Here are the answer choices:

a)3
b)8
c)10
d)5
e)none of these

Hello, alaricepent!

Make a sketch, then baby-talk your way through it . . .

Suppose the length of a rectangle is twice the width.
If we increase both the width and length of the rectangle by 2 units,
the area is increased by 34 square units.
Find the width of the rectangle.

. .

Code:

            2x
      *-------------*
      |             |
    x |             | x
      |             |
      *-------------*
            2x

Let = width
Then = length.
. . The area is: .

Code:

             2x+2
      *-------------*---*
      |             :   |
      |             :   |
 x+2  |             :   | x+2
      * - - - - - - *   |
      |                 |
      *-----------------*
             2x+2

Now = width
and = length
. . The area is: .


The new area is 34 more than the original area:
. .

So we have: .


The width is 5 . . . answer (d)