Question 777839: the area of a rectangular box is 33cm2.If the width is 8 cm less than the length. what are the dimensions
Answer by paul2007(1)   (Show Source):
You can put this solution on YOUR website! Area of the rectangle is 33 cm^2
the width is 8 cm less than the length
Let the length be, x cm
therefore, the width is (x-8)cm
we know, area of a rectangle is= length*width
according to the problem,
x*(x-8)=33
or, x^2-8x=33
or, x^2-8x-33=0
or, x^2-(11-3)x-33=0 [Middle term factor]
or, x^2-11x+3x-33=0
or, x(x-11)+3(x-11)=0
or, (x-11)(x+3)=0
now, between these two factor either one should be zero
so, 1st factor, x-11=0
or, x=11
2nd factor, x+3=0
or, x=(-3) [this value is not possible, because length cannot have negative value]
so, x=11
length of the rectangle is 11 cm
therefore, width=(length -8)cm
width=(11-8)cm=3cm
Answer: Dimension of the rectangle is length=11cm, width=3cm
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