SOLUTION: The length of a rectangle is 2 meters more than 4 times the width. If the area is 156 square meters, find the width and the length. Width:______meters Length:_____meters

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: The length of a rectangle is 2 meters more than 4 times the width. If the area is 156 square meters, find the width and the length. Width:______meters Length:_____meters      Log On


   

Question 1154961: The length of a rectangle is 2 meters more than 4 times the width. If the area is 156 square meters, find the width and the length.
Width:______meters
Length:_____meters
Found 2 solutions by mananth, ikleyn:
Answer by mananth(16946) About Me  (Show Source):
You can put this solution on YOUR website!
let width be x
length =4x+2
Area = x(4x+2)=156
4x^2+2x-156=0
2x^2+x-78=0
(2x+13)(x-6)=0
Ignore negative
x=6
width = 6
plug x to find length

Answer by ikleyn(52932) About Me  (Show Source):
You can put this solution on YOUR website!
.


With Algebra solution, you quickly come to equation

    x*(4x+2) = 156.


Multiply both sides by 4

    4x*(4x+2) = 624.


Find the decomposition of the number 624 into the product of 2 factors with the difference of 2.


    sqrt%28624%29 = 25 (approximately) will help you:  the numbers are  24 and 26.


So, 4x = 24  and x = 24/4 = 6.


ANSWER.  The dimensions are  6 and 4*6+2 = 26.


CHECK.  6*26 = 156.     ! Correct !

Solved.

Thus I solved the problem (practically, MENTALLY) without solving quadratic equation.