SOLUTION: the length of a rectangle is 1 cm less than 3 times the width. The rectangle has an area of 24 square cm. find the exact length of a diagonal of this rectangle

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Question 729293: the length of a rectangle is 1 cm less than 3 times the width. The rectangle has an area of 24 square cm. find the exact length of a diagonal of this rectangle
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
x = length
y = width
x = -1+3y
d = diagonal

AREA, %283y-1%29y=24
FIND DIAGONAL, d.
d%5E2=x%5E2%2By%5E2
d%5E2=%283y-1%29%5E2%2By%5E2
d=sqrt%28%283y-1%29%5E2%2By%5E2%29

Using area equation, first find y.
3y%5E2-y=24
3y%5E2-y-24=0
for practical purposes, highlight%28y=3%29. (used general quadratic solution formula).

Using formula just found for d, diagonal, d=sqrt%28%283%2A3-1%29%5E2%2B3%2A3%29, highlight%28d=sqrt%2873%29%29, the Diagonal.