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Value of an Expression

if the area o...

Question

if the area of a rectangle is 8x²-45y square+18xy and one of its sides is 4x+15y,find the length of adjacent sides.

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Solution

$Area of rectangle = 8 x^{2} - 45 y^{2} + 18 x y One of the sides of rectangle = 4 x + 15 y then, length of the adjacent side = \frac{area of rectangle}{one side of rectangle} = \frac{8 x^{2} - 45 y^{2} + 18 x y}{(4 x + 15 y)} = \frac{8 x^{2} + 18 x y - 45 y^{2}}{(4 x + 15 y)} = \frac{8 x^{2} + 30 x y - 12 x y - 45 y^{2}}{(4 x + 15 y)} = \frac{2 x (4 x + 15 y) - 3 y (4 x + 5 y)}{(4 x + 15 y)} = \frac{(4 x + 15 y) (2 x - 3 y)}{(4 x + 15 y)} = (2 x - 3 y) Hence, the length of adjacent side = (2 x - 3 y) units .$

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