Question 239043
A  rectangle  is  3  times  as  long  as  it  is  wide.  If  the  length  and  the  width  are  both  decreased  by  4  cm,  the  resulting  rectangle  has  area  28cm  squared.  Find  the  dimensions  of  the  original  rectangle.


L = 3W

(L-4) * (W-4) = 28


Replace L with 3W to get:


(3W-4) * (W-4) = 28


remove parentheses by multiplying out the factors to get:


3W^2 - 16W + 16 = 28


subtract 28 from both sides to get:


3W^2 - 16W - 12 = 0


this factors out to:


(3W+2) * (W-6) = 0


This makes 3W = -2 or W = 6


W can't be negative so W = 6 is the only valid answer.


if W = 6, then L = 3W makes L = 18


You have L = 18 and W = 6


substitute in the original equation to get:


(L-4) * (W-4) = 28 becomes:


(18-4) * (6-4) = 28 which becomes:


14 * 2 = 28 which becomes:


28 = 28 which is true so the values for L and W must be good.


Your answers are:


L = 18 and W = 6