Results 1 to 2 of 2

Thread: rectangle

  1. #1
    Member
    Joined
    Jan 2008
    Posts
    173

    rectangle

    The length, L, of a rectangle is increased by 50% and the width, W, is doubled to form a larger rectangle with an area of 30 cm2. What is the largest possible perimeter of the larger rectangle if L and W are integers with L > W?

    (A) 22 cm (B) 23 cm (C) 26 cm (D) 34 cm (E) 43 cm
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Super Member

    Joined
    May 2006
    From
    Lexington, MA (USA)
    Posts
    12,028
    Thanks
    849
    Hello, sri340!

    The length $\displaystyle L$ of a rectangle is increased by 50% and the width $\displaystyle W$
    is doubled to form a larger rectangle with an area of 30 cm².

    What is the largest possible perimeter of the larger rectangle
    if $\displaystyle L$ and $\displaystyle W$ are integers with $\displaystyle L > W$ ?

    . . $\displaystyle \text{(A) 22 cm} \quad\text{(B) 23 cm}\quad\text{(C) 26 cm} \quad \text{(D) 34 cm} \quad \text{(E) 43 cm}$

    The new rectangle has length $\displaystyle \tfrac{3}{2}L$ and width $\displaystyle 2W$.

    Its area is 30 cm²: .$\displaystyle \left(\tfrac{3}{2}L\right)(2W) \:=\:30 \quad\Rightarrow\quad LW \:=\:10 $


    Since $\displaystyle L$ and $\displaystyle W$ are integers with $\displaystyle L > W$
    . . there are only two possible cases:

    . . $\displaystyle \begin{array}{ccc}\text{Length} & \text{Width} & \text{Perimeter} \\ \hline
    10 & 1 & 22 \\ 5 & 2 & 14 \end{array}$


    The largest perimeter is 22 cm . (A)

    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 6
    Last Post: Jun 2nd 2011, 04:56 PM
  2. rectangle
    Posted in the Geometry Forum
    Replies: 1
    Last Post: Jan 25th 2010, 12:52 PM
  3. Replies: 1
    Last Post: Nov 23rd 2009, 06:41 PM
  4. rectangle box
    Posted in the Geometry Forum
    Replies: 1
    Last Post: Nov 17th 2008, 10:03 PM
  5. Fitting rectangle in a rectangle.
    Posted in the Geometry Forum
    Replies: 1
    Last Post: Oct 11th 2008, 06:31 PM

Search Tags


/mathhelpforum @mathhelpforum