Represent the following situation in the form of the quadratic equation:
The area of a rectangular plot is $528 m^{2}$ . The length of the plot is one metre more than twice its breadth. We need to find the length and breadth of the plot.

Question

Represent the following situation in the form of the quadratic equation:
The area of a rectangular plot is

528 m^{2}

. The length of the plot is one metre more than twice its breadth. We need to find the length and breadth of the plot.

Filo · Accepted Answer

Let the breadth of the rectangular plot (b) be

’ x ’ m .

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

∴ Length (l)

= 2 x + 1 m .

But Length

\times

Breadth = Area of rectangle

l \times b = A

∴

x \times (2 x + 1) = 528 s q . m .

2 x^{2} + x = 528

∴

2 x^{2} + x -528 = 0

is the required equation.

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

2 x^{2} + x -528 = 0

2 x^{2} -32 x + 33 x -528 = 0

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

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

If

x -16 = 0

, then

x = 16

If

2 x + 33 = 0

, then

x = - 33/2

∴ Breadth (b)

= 16 m

.

Length (l)

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

∴ Length (l)

= 33 m

Breadth (b)

= 16 m

.

Question Text	Represent the following situation in the form of the quadratic equation: The area of a rectangular plot is $528 m^{2}$ . The length of the plot is one metre more than twice its breadth. We need to find the length and breadth of the plot.
Answer Type	Text solution:1
Upvotes	150

Text solutionVerified