Math, asked by AnanyaBaalveer, 10 hours ago

What is the area of square if the area of the square is equals to the perimeter of the rectangle of dimensions 16cm × 4cm.Also find the side and perimeter of square.​

Answers

Answered by mathdude500
34

\large\underline{\sf{Solution-}}

Let us assume that side of the square be x cm.

Given that,

Area of the square is equals to the perimeter of rectangle of dimensions 16 cm × 4 cm.

Now, Length of rectangle = 16 cm

And, Breadth of rectangle = 4 cm

We know,

\boxed{ \rm{ \:Perimeter_{(Rectangle)} = 2(Length + Breadth) \: }} \\

On substituting the values, we get

\rm \: Perimeter_{(Rectangle)} = 2(16 + 4) \\

\rm \: Perimeter_{(Rectangle)} = 2 \times 20 \\

\bf\implies \: Perimeter_{(Rectangle)} = 40 \: cm \\

Now, area of the square is equals to the perimeter of the rectangle.

So,

\rm\implies \:\boxed{ \rm{ \:\bf\: Area_{(Square)} = 40\:  {cm}^{2}  \: }}\\

Now, we know,

\rm \: Area_{(Square)} =  {x}^{2}  \\

\rm \:  {x}^{2} = 40 \\

\rm \: x =  \sqrt{40}  \\

\rm \: x =  \sqrt{2 \times 2 \times 10}  \\

\bf\implies \:x = 2\sqrt{10} \: cm \\

Now,

\rm \: Perimeter_{(Square)} = 4 \times x \\

\rm \: Perimeter_{(Square)} = 4 \times 2 \sqrt{10}  \\

\bf\implies \:Perimeter_{(Square)} = 8 \sqrt{10} \: cm \\

\rule{190pt}{2pt}

Additional Information :-

\begin{gathered}\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 Base\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}d\sqrt {4a^2-d^2}\\ \\ \star\sf Parallelogram =Base\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}\end{gathered}

Answered by missattitudequeen77
9

In a square the length is equal to breadth.

Hence, area of a square = side × side

The number of 1 cm squares enclosed = 4

Area = 4 sq cm

4 = 2 × 2

Hence, area = side × side

hope its help u

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