SOLUTION: The length of a rectangle is 1 m less than twice the width. The area of the rectangle is 120 square meters. Find the length and width.

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: The length of a rectangle is 1 m less than twice the width. The area of the rectangle is 120 square meters. Find the length and width.      Log On


   

Question 203129: The length of a rectangle is 1 m less than twice the width. The area of the rectangle is 120 square meters. Find the length and width.
Answer by jojo14344(1513) About Me  (Show Source):
You can put this solution on YOUR website!


Basic Eqn --> A%5BR%5D=L%2AW

Given: system%28Width=x%2CLength=2x-1%2CA%5BR%5D=120m%5E2%29


Subst.
120m%5E2=%282x-1%29%28x%29
120m%5E2=2x%5E2-x
2x%5E2-x-120=0, remembersystem%28a=2%2Cb=-1%2Cc=-120%29

By Quadratic:
For discriminant, b%5E2-4ac=-1%5E2-4%282%29%28-120%29=1%2B960=961
Therefore,
x=%28-%28-1%29%2B-sqrt%28961%29%29%2F%282%2A2%29=%281%2B-31%29%2F4
x=%281%2B31%29%2F4=32%2F4=red%288m%29
x=%281-31%29%2F4=-30%2F4=-7.5, disregard, (-)

So, the Width=x=8meters

Also, the L=2%288%29-1=16-1
Length=15meters

Checking,
A%5BR%5D=L%2AW
120%5Em2=%2815m%29%288m%29
120m%5E2=120m%5E2

Thank you,
Jojo