SOLUTION: the width of a rectangle is 2 units less than its length. if the diagonal of the rectangle is 10 units long, find the dimensions of the rectangle.

Algebra ->  Algebra  -> Trigonometry-basics -> SOLUTION: the width of a rectangle is 2 units less than its length. if the diagonal of the rectangle is 10 units long, find the dimensions of the rectangle.      Log On

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

   

Question 108496: the width of a rectangle is 2 units less than its length. if the diagonal of the rectangle is 10 units long, find the dimensions of the rectangle.
Answer by HyperBrain(694) About Me  (Show Source):
You can put this solution on YOUR website!
The Phytagorean Theorem can be applied!
Let a=x(the length)
____b=x-2(the width)
____c=10

Thus,
x%5E2%2B%28x-2%29%5E2=10%5E2
x%5E2%2B%28x%28x-2%29-2%28x-2%29%29=100
x%5E2%2B%28%28x%5E2-2x%29-%282x-4%29%29=100
x%5E2%2B%28x%5E2-2x-2x-4%29=100
x%5E2%2Bx%5E2-4x-4=100
2x%5E2-4x-4=100
2x%5E2-4x-104=0
By the quadratic formula,
x=%284%2B-sqrt%284%5E2-4%2A2%2A%28-104%29%29%29%2F%282%2A2%29
x=%284%2B-sqrt%2816%2B832%29%29%2F%284%29
x=%284%2B-sqrt%28848%29%29%2F%284%29
x=%284%2B-+29.120439557122%29%2F%284%29
We will eliminate the x=%284-29.120439557122%29%2F%284%29 part 'coz it will be only negative---an impossible result
Continuing,
x=%284%2B29.120439557122%29%2F%284%29=33.120439557122%2F4=8.2801098892805
Thus, the length is 8.2801098892805 units long
If x=8.2801098892805, then x+2=10.2801098892805
Thus, the width is 10.2801098892805 units long

Power up,
HyperBrain!