SOLUTION: The perimeter of a rectangle is 20 inches. The area is 16 square inches. Find the dimensions.
Your supposed to solve using a quadratic formula if that helps you at all.
Algebra.Com
Question 696061: The perimeter of a rectangle is 20 inches. The area is 16 square inches. Find the dimensions.
Your supposed to solve using a quadratic formula if that helps you at all.
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!
The perimeter of a rectangle is given by 
From this we derive 
The area is the length times the width, so area as a function of width is given by:
\ =\ w\left(\frac{P}{2}\ -\ w\right))
Which can be written
\ =\ \frac{P}{2}w\ -\ w^2)
Rearranging to standard form and multiplying through by -1:
Using the quadratic formula:
where 
, 
, and 
we have:
^2\ -\ 4(1)(A)}}{2(1)})
Just plug in your given values for Perimeter and Area and then do the arithmetic. One of the roots will be the length (by convention the larger value) and the other will be the width.
John
Egw to Beta kai to Sigma
My calculator said it, I believe it, that settles it
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