SOLUTION: The length of a rectangle is 3cm more than twice the width. The area is 1890cm^2. find the length and the width of the rectangle.

Question 767096: The length of a rectangle is 3cm more than twice the width. The area is 1890cm^2. find the length and the width of the rectangle.
Found 2 solutions by solver91311, suruman:
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!

If a rectangle with area has a length that is units longer (or shorter if ) than times the width, , such that

and knowing that the Area is given by:

,

make the substitution:

Then solve the quadratic for

Note the use of the positive root only -- a negative width is absurd.

For your problem: , , and . Do the arithmetic.

John

My calculator said it, I believe it, that settles it

Answer by suruman(21) (Show Source): You can put this solution on YOUR website!
Let width of the rectangle be x
Length of the rectangle is 3 cm more than width = x+3
Area of the rectangle = Length * Width = x*(x+3) = 1890
x^2 + 3x = 1890
x^2 + 3x - 1890 =0
Compare this with a quadratic equation of the type ax^2 + bx + c = 0
Roots of a quadratic equation of the type ax^2 + bx + c = 0 is :
x = {-b +- D ) / 2a where D= Sqrt(b^2 - 4ac)
Determinant of the given quadratic equation is : D = sqrt(3^2 - (4*a*(-1890)))
= sqrt ( 9 +
Hence, roots of the given quadratic equation is = 87.
Thus the roots are :
x = {-3 + 87)/(2*1) = 42
or
x = (-3-87)/(2*1) = -45
As length of the rectangle is positive, ignoring the negative result, width of the rectancgle = 42cm
Length of the rectangle = 42 + 3 = 45cm

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