SOLUTION: The perimeter of a rectangle is 120 cm. The length of the diagonol is 9 cm longer than the width. What are the dimensions of the rectangle? You need to use algebra!

Algebra ->  Rectangles -> SOLUTION: The perimeter of a rectangle is 120 cm. The length of the diagonol is 9 cm longer than the width. What are the dimensions of the rectangle? You need to use algebra!      Log On


   

Question 429725: The perimeter of a rectangle is 120 cm. The length of the diagonol is 9 cm longer than the width. What are the dimensions of the rectangle? You need to use algebra!
Answer by Gogonati(855) About Me  (Show Source):
You can put this solution on YOUR website!
Solution:Let x cm the width, then the diagonal is x+9 cm, and the length of rectangle, using Pythagorean theorem will be:
L%5E2=%28x%2B9%29%5E2-x%5E2=x%5E2%2B18x%2B81-x%5E2=18x%2B81, and
L=sqrt%2818x%2B81%29
The perimeter of rectangle is:2L+2W=120 => L+W=60 Write the equation:
sqrt%2818x%2B81%29%2Bx=60 Solve the equation:
sqrt%2818x%2B81%29=60-x, squaring both sides have:
18x%2B81=x%5E2-120x%2B3600, set equation to zero.
x%5E2-138x%2B3519=0, solve the quadratic equation.
The roots that satisfy our problem is L=33.75 cm and W=26.34 cm.
Done.