Question

the area of the rectangle plot is 528 m squre. the length of the plot ( in meters) is one more than twice it's breadth.we need to find the length and breadth of the plot ​

Answer 1

Given: The length of rectangular plot is one more than twice it's breadth. & Area of park is 528 m².

Need to find: Dimensions of rectangular plot?

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❍ Let's consider breadth of rectangular plot be x m.

Then, Length of rectangular plot is (2x + 1) m.

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As we know that,

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$\star\:{\underline{\boxed{\frak{Area_{\:(rectangle)} = Length \times Breadth}}}}\\\\\\ \bf{\dag}\:{\underline{\frak{Putting\:given\:values\:in\:formula,}}}\\\\\\ :\implies\sf 528 = x \times (2x + 1)\\\\\\ :\implies\sf 528 = 2x^2 + x\\\\\\ :\implies\sf 2x^2 + x - 528 = 0\\\\\\ :\implies\sf 2x^2 - 32x + 33x - 528 = 0\\\\\\ :\implies\sf 2x(x - 16) + 33(x - 16) = 0\\\\\\ :\implies\sf (2x + 33)(x - 16) = 0\\\\\\ :\implies\sf Either\:(2x + 33) = 0\:or\:(x - 16) = 0\\\\\\ :\implies{\underline{\boxed{\frak{\purple{ x = \dfrac{-33}{2}\:;\: 16}}}}}\:\bigstar$

We know that,

• Dimensions of rectangle can't be negative.

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Hence, x = 16.

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Therefore,

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• Breadth of rectangular park, x = 16 m
• Length of rectangular park, (2x + 1) = 33 m

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$\therefore\:{\underline{\sf{Hence,\:Dimensions\:of\:rectangular\:plot\:is\:\bf{16\:m}\: \sf{and}\: \bf{33\:m}\: \sf{respectively}.}}}$

Answer 2

Answer:

Given :-

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

To Find :-

• What is the length and breadth of the plot.

Formula Used :-

$\bigstar \boxed{\sf{Area\: Of\: Rectangle =\: Length \times Breadth}}$

Solution :-

Let, the breadth of a rectangular plot is x m.

And, the length of a rectangular plot is 2x + 1 m.

According to the question by using the formula we get,

↦ $\sf x \times (2x + 1) =\: 528$

↦ $\sf {2x}^{2} + x =\: 528$

↦ $\sf {2x}^{2} + x - 528 =\: 0$

↦ $\sf {2x}^{2} - 32x + 33x - 528 =\: 0$

↦ $\sf 2x(x - 16) + 33(x - 16) =\: 0$

↦ $\sf (x - 16)(2x + 33) =\: 0$

↦ $\sf x - 16 =\: 0$

↦ $\sf\bold{\pink{x =\: 16}}$

Either,

↦ $\sf 2x + 33 =\: 0$

↦ $\sf 2x =\: - 33$

➠ $\sf\bold{\pink{x =\: \dfrac{- 33}{2}}}$

We can't take length and breadth as negative (- ve).

Then x = 16.

Now, we have to find the length and breadth of a rectangular plot :

$\longmapsto$ Breadth of a rectangular plot :

$\implies$ $\sf x\: m$

$\implies$ $\sf\bold{\red{16\: m}}$

$\longmapsto$ Length of a rectangular plot :

$\implies$ $\sf 2x + 1\: m$

$\implies$ $\sf 2(16) + 1\: m$

$\implies$ $\sf 32 + 1\: m$

$\implies$ $\sf\bold{\red{33\: m}}$

$\therefore$ The length and breadth of a rectangular plot is 33 m and 16 m respectively.