Reprsent the following situations in the form of quadratic equations :

1.	Reprsent the following situations in the form of quadratic equations : The area of a rectangular plot is 528 m2. The length of the plot (in metres) is one more than twice its breadth. We need to find the length and breadth of the plot.
Answer» Let the breadth of rectangular plot (b) be ’x’ m. Then the length of th plot is one more than twice its breadth, ∴ Length (l)= 2x + 1 m. But Length × Breadth = Area of rectangle l × b = A ∴ x × (2x + 1) = 528 sq.m. 2x² + x = 528 ∴ 2x² + x – 528 = 0 is the required equation. Now, we have to find out the value of ‘x’ : 2x² + x – 528 = 0 2x² – 32x + 33x – 528 = 0 2x(x – 16) + 33(x – 16) = 0 (x – 16) (2x + 33) = 0 If x – 16 = 0, then x = 16 If 2x + 33 = 0, then x = -33/2 ∴ Breadth (b) = 16 m. Length (l) = (2x + 1) = 2(16) + 1 = 32 + 1 = 33m ∴ Length (l) = 33 m Breadth (b) = 16 m.

Reprsent the following situations in the form of quadratic equations : The area of a rectangular plot is 528 m2. The length of the plot (in metres) is one more than twice its breadth. We need to find the length and breadth of the plot.

Answer»

Let the breadth of rectangular plot (b) be ’x’ m.

Then the length of th plot is one more than twice its breadth,

∴ Length (l)= 2x + 1 m.

But Length × Breadth = Area of rectangle l × b = A

∴ x × (2x + 1) = 528 sq.m.

2x² + x = 528

∴ 2x² + x – 528 = 0 is the required equation.

Now, we have to find out the value of ‘x’ :

2x² + x – 528 = 0

2x² – 32x + 33x – 528 = 0

2x(x – 16) + 33(x – 16) = 0

(x – 16) (2x + 33) = 0

If x – 16 = 0, then x = 16

If 2x + 33 = 0, then x = -33/2

∴ Breadth (b) = 16 m.

Length (l) = (2x + 1) = 2(16) + 1 = 32 + 1 = 33m

∴ Length (l) = 33 m

Breadth (b) = 16 m.