SOLUTION: The diagonal of a rectangle is four times the width. Simplify an expression for the length in terms of the width.

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Question 730996: The diagonal of a rectangle is four times the width. Simplify an expression for the length in terms of the width.
Answer by fcabanski(1391) About Me  (Show Source):
You can put this solution on YOUR website!
d=4w and width = w.


The Pythagorean theorem describes the relationship between the two legs ( a and b) of a right triangle and the hypotenuse (c). In a rectangle, the length and width are the legs, while the diagonal is the hypotenuse.


Pythagorean Theorem: a%5E2+%2B+b%5E2+=+c%5E2


General Rectangle: l%5E2+%2B+w%5E2+=+d%5E2


This specific rectangle with d = 4w: l%5E2+%2B+w%5E2+=+%284w%29%5E2+=+16w%5E2


Solve for l: l%5E2+=+16w%5E2+-+w%5E2=+15w%5E2


l=sqrt%2815w%5E2%29=w%2Asqrt%2815%29

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