Give possible expressions for the length and breadth of rectangle whose area is 25 x square + 30 x y + 9 y square - 4 z square
Answers
length = (5x + 3y + 2z) and breadth = (5x +3y - 2z)
it is given that area of rectangle is 25x² + 30xy + 9y² - 4z².
= 25x² + 30xy + 9y² - 4z²
= (5x)² + 2(5x)(3y) + (3y)² - (2z)²
[ from algebraic identity, a² + 2ab + b² = (a + b)² ]
= (5x + 3y)² - (2z)²
[ using algebraic identity, a² - b² = (a + b)(a - b) ]
= {(5x + 3y) + (2z)}{(5x + 3y) - (2z)}
= (5x + 3y + 2z)(5x + 3y - 2z)
so, area of rectangle is (5x + 3y + 2z)(5x + 3y - 2z) ........(1)
we know, area of rectangle = length × breadth........(1)
on comparing we get,
length = (5x + 3y + 2z)
and breadth = (5x + 3y - 2z)
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