Question

The area of a square park is same as that of a rectangular park.If the side of the square park is 80 m and the length of the rectangular park is 100m, find the breadth of the rectangular park . ​

Answer 1

Solution:

Area of square park = area of rectangular park (given)

Side of square park = 80m

We know, area of square = $side^{2}$ $unit^{2}$

∴ area of square park = 80 × 80 sq.m = 6400 sq.m

∴ area of rectangular park = 6400 sq.m

Length of rectangular park = 100m

We know, breadth of rectangle = $\frac{area}{length}$ unit

∴ breadth of rectangular park = (6400/100)m

= 64m

Answer: breadth of the rectangular park is 64m.

Answer 2

❍ Let's Consider b be the Breadth of Rectangular Park.

$\dag\frak{\underline {As,\:We\:know\:that::\:}}$

$\star\boxed{\pink{\sf{ Area\:of \:Square \:= Side \times Side }}}$

And ,

$\star\boxed{\pink{\sf{ Area\:of \:Rectangle \:= Length \times Breadth }}}$

Given that ,

• The area of a square park is same as that of a rectangular park.

Or ,

• Area of Square Park = Area of Rectangular Park .

Or ,

• $\implies \sf{ Side \times Side = Length \times Breadth}$

Where,

• Side of Square Park is 80 m & Length of Rectangular Park is 100 m.

⠀⠀⠀⠀⠀⠀$\underline {\bf{\star\:Now \: By \: Substituting \: the \: Given \: Values \::}}$

$:\implies \sf{ 80 \times 80 = 100 \times b} \\\\\\ :\implies \sf{ 6,400 = 100 \times b} \\\\\\ :\implies \sf{ b = \cancel{\dfrac{6400}{100}} }\\\\\\\underline {\boxed{\pink{ \mathrm {  b = 64\: m}}}}\:\bf{\bigstar}$

Therefore,

⠀⠀⠀⠀⠀$\therefore {\underline{ \mathrm {  Hence,\:Breadth \:of\:Rectangular \:Park\:is\:\bf{64\: m}}}}$

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$\large {\boxed{\sf{\mid{\overline {\underline {\star More\:To\:know\::}}}\mid}}}$

• $\begin{gathered}\boxed{\begin {array}{cc}\\ \dag\quad \Large\underline{\bf Formulas\:of\:Areas:-}\\ \\ \star\sf Square=(side)^2\\ \\ \star\sf Rectangle=Length\times Breadth \\\\ \star\sf Triangle=\dfrac{1}{2}\times Breadth\times Height \\\\ \star \sf Scalene\triangle=\sqrt {s (s-a)(s-b)(s-c)}\\ \\ \star \sf Rhombus =\dfrac {1}{2}\times d_1\times d_2 \\\\ \star\sf Rhombus =\:\dfrac {1}{2}p\sqrt {4a^2-p^2}\\ \\ \star\sf Parallelogram =Breadth\times Height\\\\ \star\sf Trapezium =\dfrac {1}{2}(a+b)\times Height \\ \\ \star\sf Equilateral\:Triangle=\dfrac {\sqrt{3}}{4}(side)^2\end {array}}\end{gathered}$

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