SOLUTION: The diagonal of a rectangle is 3 ft longer than the length of the rectangle and 4 ft longer than twice the width. Find the dimensions of the rectangle.

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Question 1131622: The diagonal of a rectangle is 3 ft longer than the length of the rectangle and 4 ft longer than twice the width. Find the dimensions of the rectangle.
Found 2 solutions by MathLover1, ikleyn:
Answer by MathLover1(20850)   (Show Source): You can put this solution on YOUR website!

if the diagonal of a rectangle is ft longer than the length of the rectangle and ft longer than the width , we have


=>
=>
=>

Find the dimensions of the rectangle:
we can only do this


because neither perimeter nor area is given

Answer by ikleyn(52788)   (Show Source): You can put this solution on YOUR website!
.
One equation is 

   L = 2W + 1,       (1)

as the tutor @LoverMath1 derived in her post.


The other equation is

     = 2W + 4.

which follows from the condition.


This second condition, due to (1), is the same as

     = 2W + 4.     (2)


Equation (2) is your basic equation to solve.   Square both sides

    W^2 + 4W^2 + 4W + 1 = 4W^2 + 16W + 16

    W^2 - 12W - 15 = 0.


Answer.  The dimensions of the rectangle are  W =   and  L = 2W+1 =  feet.


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