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 ?
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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) (Show Source): You can put this solution on YOUR website!
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:
^2\ +\ w^2\ =\ 169)
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
My calculator said it, I believe it, that settles it
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