Question

01 quadratic equations :
(1) 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 1

Given :-

• The area of a rectangular plot is 528 m². The length of the plot (in metres) is one
• more than twice its breadth.

To find :-

• Length and breadth of the plot

Solution :-

Let the breadth of plot be x then length be (2x + 1)

• Area of rectangular plot = 528 m²

→ Length × breadth = 528

→ (2x + 1)x = 528

→ 2x² + x = 528

→ 2x² + x - 528 = 0

Apply quadratic formula

• a = 2
• b = 1
• c = - 528

→ D = b² - 4ac

→ D = (1)² - 4 × 2 × (-528)

→ D = 1 + 4224

→ D = 4225

• x = - b ± √D/2a

→ x = 1 ± √4225/2 × 2

→ x = 1 ± 65/4

Either

→ x = - 1 - 65/4

→ x = - 66/4

→ x = - 33/2

Or

→ x = -1 + 65/4

→ x = 64/4

→ x = 16

• Length or breadth never in negative

Hence,

• Breadth of rectangular plot = x = 16m
• Lenght of rectangular plot = 2x + 1 = 33m

Answer 2

Solution :

• Let the Breadth be b

• Then, length will be 2b + 1

• It is given that Area of reactangular plot is 528 m².

According to question now :

Area = Length × Breadth

528 = (b) (2b + 1)

528 = 2b² + b

2b² + b - 528 = 0

Now, by using middle splitting term we get,

2b² - 32b + 33b - 528 = 0

2b (b - 16) + 33 (b - 16) = 0

(2b + 33) (b - 16) = 0

If x - 16 = 0, then x = 16

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

Therefore, Breadth = 16 meter.

So,

Length = 2b + 1 = 2(16) + 1 = 32 + 1 = 33 m

Therefore,

• Length of the reactangular plot = 33 m

• Breadth of the reactangular plot = 16 m