SOLUTION: Geometry. The length of a rectangle is 1 cm longer than its width. If the diagonal of the rectangle is 4 cm, what are the dimensions (the length and the width) of the rectangle?

Algebra ->  Algebra  -> Rectangles -> SOLUTION: Geometry. The length of a rectangle is 1 cm longer than its width. If the diagonal of the rectangle is 4 cm, what are the dimensions (the length and the width) of the rectangle?       Log On

Ad: Algebrator™ solves your algebra problems and provides step-by-step explanations!
Ad: Algebra Solved!™: algebra software solves algebra homework problems with step-by-step help!

   

Question 47837: Geometry. The length of a rectangle is 1 cm longer than its width. If the diagonal of the rectangle is 4 cm, what are the dimensions (the length and the width) of the rectangle?
Thanks!
Answer by venugopalramana(3286) About Me  (Show Source):
You can put this solution on YOUR website!
The length of a rectangle is 1 cm longer than its width.
LET WIDTH =W
LENGTH=W+1
If the diagonal of the rectangle is 4 cm, what are the dimensions (the length and the width) of the rectangle?
DIAGONAL^2=L^2+W^2
4^2=(W+1)^2+W^2
W^2+2W+1+W^2=16
2W^2+2W-15=0
w+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
w+=+%28-2+%2B-+sqrt%28+2%5E2-4%2A2%2A%28-15%29+%29%29%2F%282%2A2%29+
w+=+%28-2+%2B-+sqrt%28+4%2B120+%29%29%2F%284%29+
w+=+%28-2+%2B2%2Asqrt%28+31+%29%29%2F%284%29+=2.28
W=2.28 AND L=3.28
Thank You!