SOLUTION: A rectangular garden has a perimeter of 34. There is a diagonal line crossing to the other side with the length of 13. What is the length and width of the garden ?

Algebra ->  Pythagorean-theorem -> SOLUTION: A rectangular garden has a perimeter of 34. There is a diagonal line crossing to the other side with the length of 13. What is the length and width of the garden ?      Log On


   

Question 350235: A rectangular garden has a perimeter of 34. There is a diagonal line crossing to the other side with the length of 13. What is the length and width of the garden ?
Answer by solver91311(24713) About Me  (Show Source):
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The perimeter of a rectangle is given by:



So if the perimeter is 34, then



Which is to say



and furthermore:



The diagonal of a rectangle forms the hypotenuse of a right triangle where the legs are the length and width of the rectangle. So, Mr. Pythagoras says, if the hypotenuse is 13 and the legs are and , then:



Substituting:



Expand, collect like terms, and factor to solve for . One of the roots will be the length and the other will be the width.

John

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