SOLUTION: a rectangle has a length twice its width. A square with the same area has a side 2 units longer than the width of the rectangle. Find the dimensions of the rectangle.

Algebra ->  Trigonometry-basics -> SOLUTION: a rectangle has a length twice its width. A square with the same area has a side 2 units longer than the width of the rectangle. Find the dimensions of the rectangle.      Log On


   

Question 108499: a rectangle has a length twice its width. A square with the same area has a side 2 units longer than the width of the rectangle. Find the dimensions of the rectangle.
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
a rectangle has a length twice its width.
A square with the same area has a side 2 units longer than the width of the rectangle.
Find the dimensions of the rectangle.
------------
Let width of rectangle be "x"
Then length of rectangle is "2x"
Area of rectangle is 2x^2
--------------
Square area = (side)^2 = 2x^2
Side of square = xsqrt(2)
------------------
EQUATION:
side ofsquare = width of rectangle + 2
xsqrt(2) = x+2
Square both sides to get:
2x^2 = x^2+4x+4
x^2-4x-4=0
x = [4 +- sqrt(16-4*-4)]/2
x = [4 +- sqrt(32)]/2
x = [2 +- 2sqrt(2)]
x = 2(1+sqrt(2)) or approximately 4.828...(this is the width of the rectangle)
==============
Cheers,
Stan H.