Question

2. The length of a rectangular plot of land is
twice its breadth. A square swimming pool
of side 8 m, occupies one-eighth part of the
plot. The length of the plot is [JNV 2019]
(1) 64 m
(2) 32 m
(3) 16 m
(4) 12 m​

Answer 1

Answer :

• Length of rectangular plot is 32m

Given :

• The length of a rectangular plot of land is twice its breadth
• A square swimming pool of side is 8m occupies one - eighth part of the plot

To find :

• Length of the plot

Solution :

• Breadth of rectangular be x

Given, the length of a rectangular plot of land is twice its breadth so,

• Length of rectangular be 2x

And also Given that,a square swimming pool of side 8m occupies one - eighth part of the plot so,

• Area of swimming pool = 1/8 × area of rectangular plot of land

Substituting the value :

➞ (side)² = 1/8 × length × breadth

➞ (8)² = 1/8 × 2x × x

➞ 64 = 1/4 × x²

➞ 64 × 4 = x²

➞ x² = 64 × 4

➞ x² = 256

➞ x = √256

➞ x = 16 m

• Breadth of rectangular plot is 16m

Finding the length of plot :

➞ 2x

➞ 2(16)

➞ 32m

Hence , Length of rectangular plot is 32m

Answer 2

☯ Let Breadth of the Rectangular plot of Land B.

☯ Then Length of land will be 2B.

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$\:\:\:\:\:{\underline{\sf{\bf{\bigstar\:According\:to\:the\:given\:Question:}}}}$

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• A square swimming pool of side 8m occupies one - eighth part of the plot.

• It Means, Area of Swimming Pool = $\:{\sf{\dfrac{\bold 1}{\bold 8}}\:\times\:Area\:of\:Rectangular\:Land}$

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$\:\:\:\circledcirc\:\sf{\underline{\bold{Side\:length}^{\bold 2}\:{=\:{\dfrac{1}{8}}\:\times\:l\:\times\:b}}}$

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$\:\:\:\:\:\:\dashrightarrow\:\sf{8m}^{2}\:=\:{\dfrac{1}{8}}\:\times\:2B\:\times\:B$

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$\:\:\:\:\:\:\dashrightarrow\:\sf{64\:=\:{\dfrac{1}{4}}\:\times\:B}^{2}$

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$\:\:\:\:\:\:\dashrightarrow\:\sf{64\:\times\:4\:=\:B}^{2}$

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$\:\:\:\:\:\:\dashrightarrow\:\sf{B\:=\:16m}$

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• So, Breadth of Rectangular Plot of land is 16m and Length of Rectangular Land is 2 $\:\times\:$16 = 32m.

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$\:\:\:\:\:\:\therefore\:{\underline{\sf{Hence,\: the\:length\:of\:the\:plot\:is\:{\textsf{\textbf { 32m }}}}}}.$

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