Question

the length of a rectangular lot is twice its width. the area of the lot is 242 square meters. what are the dimensions of the lot?

Answer 1

Appropriate Question:

• The length of a rectangular plot is twice its width. the area of the plot is 242 m². what are the dimensions of the plot?

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Given:

• Length of rectangular plot is twice its breadth.
• Area of rectangular plot = 242 m².

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To find:

• Dimensions of rectangular plot?

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Solution:

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☯ Let breadth of rectangular plot be x.

Therefore, Length of rectangular plot is 2x.

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$\setlength{\unitlength}{1cm}\begin{picture}(0,0)\thicklines\multiput(0,0)(5,0){2}{\line(0,1){3}}\multiput(0,0)(0,3){2}{\line(1,0){5}}\put(0.03,0.02){\framebox(0.25,0.25)}\put(0.03,2.75){\framebox(0.25,0.25)}\put(4.74,2.75){\framebox(0.25,0.25)}\put(4.74,0.02){\framebox(0.25,0.25)}\multiput(2.1,-0.7)(0,4.2){2}{\sf\large 2x m}\multiput(-1.4,1.4)(6.8,0){2}{\sf\large x m}\put(-0.5,-0.4){\bf A}\put(-0.5,3.2){\bf D}\put(5.3,-0.4){\bf B}\put(5.3,3.2){\bf C}\end{picture}$

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$\underline{\bigstar\:\boldsymbol{According\:to\:the\:question\::}}$

• Area of rectangular plot = 242 m².

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$\dag\;{\underline{\frak{As\;we\;know\;that,}}}$

$\star\;{\boxed{\sf{\pink{Area_{\;(rectangle)} = length \times breadth}}}}$

$:\implies\sf Length \times breadth = 242$

$:\implies\sf 2x \times x = 242$

$:\implies\sf 2x^2 = 242$

$:\implies\sf x^2 = \cancel{ \dfrac{242}{2}}$

$:\implies\sf x^2 = 121$

$:\implies\sf \sqrt{x^2} = \sqrt{121}$

$:\implies{\underline{\boxed{\frak{\purple{x = 11}}}}}\;\bigstar$

Therefore,

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• Breadth of rectangular plot, x = 11 m
• Length of Rectangular plot, 2x = 2 × 11 = 22 m

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$\qquad\qquad\boxed{\underline{\underline{\pink{\bigstar \: \bf\:More\:to\:know\:\bigstar}}}}$

$\begin{array}{|c|c|c|}\cline{1-3}\bf Shape&\bf Area\ formula&\bf Perimeter\ formula\\\cline{1-3}\sf Square&\tt side \times side}&\tt 4 \times side\\\cline{1-3}\sf Rectangle&\tt length \times breadth&\tt 2(length + breadth)\\\cline{1-3}\sf Triangle&\tt \dfrac{1}{2} \times base \times height&\tt sum\of\ all\ sides\ of\ \triangle\\\cline{1-3}\end{array}$

Answer 2

Answer:

$Given$

• The length of a rectangular plot is twice its width. The area of the plot is 24 m².

$To\: Find$

• What are the dimensions of the plot.

Solution :-

Let, the breadth be x and length be 2x

Area of the dimension is 24 m²

We know that,

✠ Area = Length × Breadth ✠

ATQ,

⇥ 242 = 2x × x

⇥ 242 = 2x²

⇥ 2x² = 242

⇥ x² = $\dfrac{242}{2}$

⇥ x² = 121

⇥ x = $\sqrt{121}$

➡ x = 11

Hence, the required length and breadth are,

• Breadth = x = 11 m
• Length = 2x = 2(11) = 22 m

Therefore, the breadth and length of a rectangular plot is 11 m and 22 m respectively.