SOLUTION: Suppose that the length of a certain rectangle is 2 cm more than three times its width. If the area of the rectangleis 56 square centimeters, find its length and width.

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: Suppose that the length of a certain rectangle is 2 cm more than three times its width. If the area of the rectangleis 56 square centimeters, find its length and width.       Log On


   

Question 23797: Suppose that the length of a certain rectangle is 2 cm more than three times its width. If the area of the rectangleis 56 square centimeters, find its length and width.
Answer by Paul(988) About Me  (Show Source):
You can put this solution on YOUR website!
let the length be y and let the width be x
y = 3x+2

Area = length x width
xy=56
x(3x+2)=56
3x%5E2%2B2x=56
3x%5E2%2B2x-56=0 --- solve for x by using quardratic formula:
x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
In ax%5E2+%2B+bx+%2B+c+=+0 a=3, b=2, c=-56
x+=+%28-2+%2B-+sqrt%28+%282%29%5E2-4%2A3%2A-56+%29%29%29%2F+2%283%29 ---> divide by 2(3)
x+=+%28-2+%2B-+sqrt%28+4%2B672%29%29%2F6%29
x+=+%28-2+%2B+sqrt%28+676%29%29%2F6%29 ---> add the foloowing don't subtrract.
x = 4
3(4)+2 = 14
Hence, the length is 14 and the width is 4.