Question

the length of the rectangle is greater than its breadth by 2 cm the area of the rectangle is 24 cm square find its length and breadth

Answer 1

Answer:

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Step-by-step explanation:

Let the breadth of the rectangle be ‘x’ cm.

∴  It’s length is (x + 2) cm.

As per the given condition.

∴  Area of rectangle = Length × Breadth

∴  24 = (x + 2) x

∴  24 = x2 + 2x

∴  0 = x2 + 2x – 24

∴  x2 + 2x – 24 = 0

∴  x2 – 4x + 6x – 24 = 0

∴  x (x – 4) + 6(x – 4) = 0

∴  (x – 4) (x + 6) = 0

∴  x – 4 = 0 or x + 6 = 0

∴  x = 4 or x = -6

∴  The breadth of rectangle cannot be negative.

∴  x cannot be negative

∴  x = 4 and

x + 2 = 4 + 2 = 6

∴  The length of rectangle is 6 cm and its breadth is 4 cm.

Answer 2

Answer:

LET LENGTH = X , AND BREADTH = Y

==> X = Y+2

AREA OF RECTANGLE = LENGTH * BREADTH

==> 24 =  X×Y

==> 24 = (Y+2)×Y

==> 24 = Y²+2Y

==> 0 = Y²+2Y-24

==> Y²+6Y-4Y-24 = 0

==> Y(Y+6)-4(Y+6) = 0

==> (Y+6)(Y-4)  = 0

==> Y = -6;4

-6 IS NOT POSSIBLE BECAUSE IT IS NEGATIVE

SO, Y = 4

==> BREADTH = 4

LENGTH ===> X = 2+Y ==> 2+4 ==> 6

SO, LENGTH = 6 , BREADTH = 4