SOLUTION: In the rectangle, the length is 3/4 more than the square of the width. When the length is reduced by 1, the area will be 3cm^2. What is the original dimension of the rectangle?

Algebra ->  Rectangles -> SOLUTION: In the rectangle, the length is 3/4 more than the square of the width. When the length is reduced by 1, the area will be 3cm^2. What is the original dimension of the rectangle?      Log On


   

Question 1106708: In the rectangle, the length is 3/4 more than the square of the width. When the length is reduced by 1, the area will be 3cm^2. What is the original dimension of the rectangle?
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
L and w for length and width

Original dimensions,
L=w%5E2%2B3%2F4
and
w

Reduced length by 1,
L-1=w%5E2%2B3%2F4-1
L-1=w%5E2-1%2F4
but same
width w.
-
This area given as 3 square units.
w%2A%28L-1%29=3
w%28w%5E2-1%2F4%29=3
w%5E3-w%2F4=3
4w%5E3-w=12
4w%5E3-w-12=0

(used graphing tool to find the single root)
highlight%28w=1.5%29
and
L=%283%2F2%29%5E2%2B3%2F4
L=9%2F4%2B3%2F4
L=12%2F4
highlight%28L=3%29