SOLUTION: The length of a rectangle is 7 feet more than its width. The length of a diagonal of the rectangle is 9 feet more than the width. By algebraic methods find the width of the rectang

Algebra ->  Rectangles -> SOLUTION: The length of a rectangle is 7 feet more than its width. The length of a diagonal of the rectangle is 9 feet more than the width. By algebraic methods find the width of the rectang      Log On


   

Question 390634: The length of a rectangle is 7 feet more than its width. The length of a diagonal of the rectangle is 9 feet more than the width. By algebraic methods find the width of the rectangle.
Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!


Hi,         

Let w ,(w+7ft),(w+9ft)represent the width,length and diagonal respectively

Using the Pytahgorean Theorem

 w^2  + (w+7)^2 = (w+9)^2

 w^2 + w^2 + 14w + 49 = w^2 + 18w + 81

   w^2 -4w - 32 = 0

factoring

 (w-8)(w+4) = 0

  (w+4) = 0

    w = -4  Tossing out negative solution for length

  (w-8) = 0

      w = 8ft,  the width of the rectangle   (length=15ft, diagonal=17ft)



CHECKING our Answer

   64 + 225 = 289