Algebra/geometry
posted by Bill on .
a rectangle has a width of 4 cm less than it's length. if a new rectangle is formed by increasing the width 5 cm and decreasing the length 3 cm, the area of this resulting rectangle is 177 cm squared. what are the dimensions of the original rectangle?

let x = length of the original rectangle
let x4 = width of the original rectangle
using the conditions given by the 2nd statement,
new width: (x4) + 5
new length: x  3
using the next condition given in the problem, and recalling that the area of a rectangle is just length*width:
(x3)[(x4) + 5] = 177
(x3)(x+1)  177 = 0
expanding this using FOIL:
x^2  2x  3  177 = 0
x^2  2x  180 = 0
we see that this one's not factorable,, so you use quadratic formula~
hope this helps :)