Find the product by using quadratic formula

1.	Find the product by using quadratic formula
Answer» Answer: QUESTION :- $\leadsto$ 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. 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 :- What is the length and breadth of the plot. Formula Used :- $\clubsuit$ Area Of Rectangle Formula : $\mapsto \sf\boxed{\bold{\pink{Area_{(Rectangle)} =\: Length \times Breadth}}}$ Solution :- Let, $\mapsto \bf Breadth_{(Rectangular\: Plot)} =\: x\: m$ $\mapsto \bf Length_{(Rectangular\: Plot)} =\: (2x + 1)\: m$ According to the question by using the formula we get, $\implies \sf 528 =\: (2x + 1) \times x$ $\implies \sf 528 =\: 2x^2 + x$ $\implies \sf 2x^2 + x - 528 =\: 0\: \: \bigg\lgroup \small\bold{\pink{This\: is\: the\: required\: quadratic\: equation}}\bigg\rgroup\\$ $\implies \sf 2x^2 + x - 528 =\: 0$ $\implies \sf 2x^2 + (33 - 32)x - 528 =\: 0$ $\implies \sf 2x^2 + 33x - 32x - 528 =\: 0\: \: \bigg\lgroup \small\bold{\pink{By\: doing\: middle\: term}}\bigg\rgroup$ $\implies \sf x(2x + 33) - 16(2x + 33) =\: 0$ $\implies \sf (x - 16)(2x + 33) =\: 0$ $\implies \bf x - 16 =\: 0$ $\implies \sf\bold{\purple{x =\: 16}}$ Either, $\implies \bf 2x + 33 =\: 0$ $\implies \sf 2x =\: - 33$ $\implies \sf\bold{\purple{x =\: \dfrac{- 33}{2}}}\: \: \bigg\lgroup \small\bold{\pink{Length\: and\: breadth\: can't\: be\: negative\: (- ve)}}\bigg\rgroup\\$ Then, we have to take x = 16. HENCE, the required length and breadth of the plot : ❒ Length Of Rectangular Plot : $\longrightarrow \sf Length_{(Rectangular\: Plot)} =\: (2x + 1)m$ $\longrightarrow \sf Length_{(Rectangular\: Plot)} =\: \{2(16) + 1\}\: m$ $\longrightarrow \sf Length_{(Rectangular\: Plot)} =\: (32 + 1)m$ $\longrightarrow \sf\bold{\red{Length_{(Rectangular\: Plot)} =\: 33\: m}}$ ❒ Breadth Of Rectangular Plot : $\longrightarrow \sf Breadth_{(Rectangular\: Plot)} =\: x\: m$ $\longrightarrow \sf\bold{\red{Breadth_{(Rectangular\: Plot)} =\: 16\: m}}$ ${\small{\bold{\underline{\therefore\: The\: length\: and\: breadth\: of\: a\: rectangular\: plot\: is\: 33\: m\: and\: 16\: m\: respectively\: .}}}}$

Answer»

Answer:

QUESTION :-

$\leadsto$ 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.

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 :-

What is the length and breadth of the plot.

Formula Used :-

$\clubsuit$ Area Of Rectangle Formula :

$\mapsto \sf\boxed{\bold{\pink{Area_{(Rectangle)} =\: Length \times Breadth}}}$

Solution :-

Let,

$\mapsto \bf Breadth_{(Rectangular\: Plot)} =\: x\: m$

$\mapsto \bf Length_{(Rectangular\: Plot)} =\: (2x + 1)\: m$

According to the question by using the formula we get,

$\implies \sf 528 =\: (2x + 1) \times x$

$\implies \sf 528 =\: 2x^2 + x$

$\implies \sf 2x^2 + x - 528 =\: 0\: \: \bigg\lgroup \small\bold{\pink{This\: is\: the\: required\: quadratic\: equation}}\bigg\rgroup\\$

$\implies \sf 2x^2 + x - 528 =\: 0$

$\implies \sf 2x^2 + (33 - 32)x - 528 =\: 0$

$\implies \sf 2x^2 + 33x - 32x - 528 =\: 0\: \: \bigg\lgroup \small\bold{\pink{By\: doing\: middle\: term}}\bigg\rgroup$

$\implies \sf x(2x + 33) - 16(2x + 33) =\: 0$

$\implies \sf (x - 16)(2x + 33) =\: 0$

$\implies \bf x - 16 =\: 0$

$\implies \sf\bold{\purple{x =\: 16}}$

Either,

$\implies \bf 2x + 33 =\: 0$

$\implies \sf 2x =\: - 33$

$\implies \sf\bold{\purple{x =\: \dfrac{- 33}{2}}}\: \: \bigg\lgroup \small\bold{\pink{Length\: and\: breadth\: can't\: be\: negative\: (- ve)}}\bigg\rgroup\\$

Then, we have to take x = 16.

HENCE, the required length and breadth of the plot :

❒ Length Of Rectangular Plot :

$\longrightarrow \sf Length_{(Rectangular\: Plot)} =\: (2x + 1)m$

$\longrightarrow \sf Length_{(Rectangular\: Plot)} =\: \{2(16) + 1\}\: m$

$\longrightarrow \sf Length_{(Rectangular\: Plot)} =\: (32 + 1)m$

$\longrightarrow \sf\bold{\red{Length_{(Rectangular\: Plot)} =\: 33\: m}}$

❒ Breadth Of Rectangular Plot :

$\longrightarrow \sf Breadth_{(Rectangular\: Plot)} =\: x\: m$

$\longrightarrow \sf\bold{\red{Breadth_{(Rectangular\: Plot)} =\: 16\: m}}$

${\small{\bold{\underline{\therefore\: The\: length\: and\: breadth\: of\: a\: rectangular\: plot\: is\: 33\: m\: and\: 16\: m\: respectively\: .}}}}$