Question

the length of a rectangle exceeds it's width by 3 cm .if the width is increased by 4 m and the length is decreased by 6 m the area is decreased by 22 sq.m. find the dimensions of the rectangle.

Answer 1

$\textbf {\huge {\underline{Hey there!}}}$


$<b>Original rectangle :$


⇒Let Breadth of the rectangle be x m


⇒ Length of the rectangle = ( x + 3 ) m


⇒ Area of the rectangle = Length × Breadth


⇒ Area of the rectangle = x( x + 3 )


⇒ Area of the rectangle = ( x^2 + 3x ) m^2


New Rectangle :


⇒ Breadth of the rectangle = ( x + 4 ) m


⇒ Length of the rectangle = ( x + 3 - 6 ) m


⇒ Length of the rectangle = ( x - 3 ) m


⇒ Area of the rectangle = ( x + 4 ) ( x - 3 )


⇒ Area of the rectangle = ( x^2 + x - 12 ) m^2


⇒ x^2 + x - 12 = x^2 + 3x - 22


⇒ x^2 + x - 12 - x^2 - 3x + 22 = 0


⇒ - 2x + 10 = 0


⇒ - 2x = - 10


⇒ x = 5


∴ Length of the rectangle = ( x + 3 ) = 8 m


∴ Breadth of the rectangle = 5 m


$\huge\bf\orange {Thanks}$


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