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Sum

Represent 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

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#### Solution

Let the breadth of the rectangular plot = x m

Hence, the length of the plot is (2x + 1) m.

Formula of area of rectangle = length × breadth = 528 m^{2}

Putting the value of length and width, we get

(2x + 1) × x = 528

⇒ 2x^{2} + x =528

⇒ 2x^{2} + x - 528 = 0

2x2 + 33x - 32x - 528 = 0

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

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

2x + 33 = 0 And x - 16 = 0

2x = -33 And x = 16

x = `(-33)/2` And x = 16

Since,

Width of rectangular plot = X m = 16 m

Length of rectangular plot = 2x + 1 m

= 2 × 16 + 1 m

= 32 + 1 m

= 33 m

Concept: Quadratic Equations

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