Question 886597: could u please help me solve this question the length of a rectangle is 4 meters more than twice its width. if the rectangle is 126 square meters,find its length and it width.
Answer by rothauserc(4718)   (Show Source):
You can put this solution on YOUR website! let w be the rectangle's width, then the rectangle's length is 2w+4
the area of a rectangle is length times width, therefore we have
126 = (2w+4) * w
126 = 2w^2 +4w
2w^2 +4w -126 = 0
now we factor this polynomial, first write down the prime factors of 126, they are
2, 3^2, 7 and we see that 18 and 7 give us the desired result
2w^2 +4w -126 = (2w+18)*(w-7) = 0
we have two solutions for w
2w+18 = 0
2w = -18
w = -9
and
w-7 = 0
w = 7
we want a positive value for w so we reject w = -9
therefore
the length = 2*7 +4 = 18 meters and the width = 7 meters
note that 18 * 7 = 126, our answer checks
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