Question

find the width of rectangle if it's area is (3x^2 + 9xy + 6y^2 ) square centimeters .

3x + 6y cm
A ----------------- D
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B-------------------C

Answer 1

Given:
Length = 3x + 6y cm
Area = 3x² + 9xy + 6y²

Because Area = Width * Length, therefore
Width = Area/Length
           = (3x² + 9xy + 6y²)/(3x + 6y).

Width = $Width= \frac{3( x^{2} +3xy+2 y^{2}) }{3(x+2y)}$
$Width=\frac{(x+y)(x+2y)}{x+2y} =x+y$

Answer:  x+y