SOLUTION: The length of a rectangle is 1 cm more than 5 times its width. If the area of the rectangle is 82 cm. find the dimensions of the rectangle to the nearest thousandth. Can you please

Algebra ->  Pythagorean-theorem -> SOLUTION: The length of a rectangle is 1 cm more than 5 times its width. If the area of the rectangle is 82 cm. find the dimensions of the rectangle to the nearest thousandth. Can you please      Log On


   

Question 338544: The length of a rectangle is 1 cm more than 5 times its width. If the area of the rectangle is 82 cm. find the dimensions of the rectangle to the nearest thousandth. Can you please help me find the formula for this problem?
Answer by mananth(16946) About Me  (Show Source):
You can put this solution on YOUR website!
let width be x
length = 5x+1
..
Area of rectangle = L*W
82=x(5x+1)
82=5x^2+x
add -82
82-82=5x^2+x-82
5x^2+x-82=0
Use the quadratic formula
%28%28-b+%2B-+sqrt%28b%5E2-4ac%29%29%2F2a%29
a=5, b=1, c=-82
x1=%28%28-1+%2B+sqrt%281%2B1640%29%29%2F10%29
= 3.951
x2= %28%28-1+-+sqrt%281%2B1640%29%29%2F10%29
x2=-4.15 (ignore negative value)
width = 3.951 cm
..
Length = 5*3.951 + 1
L = 20.755 cm.
CHECK
((5*3.951) + 1)*3.951=82