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?

Answer 1

let x = length of the original rectangle
let x-4 = width of the original rectangle

using the conditions given by the 2nd statement,
new width: (x-4) + 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:
(x-3)[(x-4) + 5] = 177
(x-3)(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 :)