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The area of a square and a rectangle are equal. If the side of the square is
50cm and breadth of the rectangle is 40 cm. find
a) Length of the rectangle
b) Perimeter of the rectangle
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[tex]\huge{\fcolorbox{maroon}{s} {\large{\fcolorbox{white}{mistyrose}{{\fcolorbox{gold} {White}{Answer}}}}}}[/tex]
Given :
There are two shapes given which is square and rectangle having same area
i.e. Area of Square = Area of Rectangle
Side of square = 50cm
Breadth (b) of rectangle = 40cm
To find :
Length and perimeter of the rectangle
Solution :
We know that,
Area of square = side × side
[tex] = > 50 \times 50 = 2500 {cm}^{2} [/tex]
----------------------------------------------------------
It is given that,
Area of rectangle = Area of square
We also know that,
Area of rectangle = length × breadth
[tex] = > length \times 40 = 2500[/tex]
[tex] = >length = \frac{2500}{40} \\ [/tex]
[tex] = > length \: (l) \: = 62.5 \: cm[/tex]
----------------------------------------------------------
We also know that,
Perimeter of rectangle = 2 × (l + b)
[tex] = > 2 \times (62.5 + 40)[/tex]
[tex] = > 2 \times 102.5[/tex]
[tex] = > 205 \: cm[/tex]
----------------------------------------------------------
Therefore,
Length of the rectangle is 62.5 cm
& perimeter of the rectangle is 205 cm.
Hope it helped you...
Thank you !!
Verified answer
GiveN:
To FinD:
SolutioN:
☼︎ Area of Rectangle;
Using Formula:
[tex]\red\bigstar {\underline{\boxed{\color{springgreen}{\textsf{ \textbf{ \: Area \: of \: Square \: = \: \: a² }}}}}}[/tex]
[tex] \sf \implies\: Area \: of \: Square= \: a^{2} [/tex]
[tex] \sf \implies\: Area \: of \: Square= \: 50^{2} [/tex]
[tex] \sf \implies\: Area \: of \: Square= \: 50 \times 50[/tex]
[tex] \sf \implies\: Area \: of \: Square =\:2500 \: cm {}^{2} [/tex]
[tex]\qquad{\rule{200pt}{2pt}}[/tex]
☼︎ Lenght of Rectangle;
Using Formula:
[tex]\blue \bigstar \: {\underline{\boxed{\color{red}{\textsf{ \textbf{Area of square = length × breadth}}}}}}[/tex]
[tex] \sf \implies\: Area \: of \: square= Length× Breadth [/tex]
[tex] \sf \implies\: 2500= Length× 40 [/tex]
[tex] \sf \implies\: Length= \frac{2500}{40} [/tex]
[tex] \sf \implies\: Length= \frac{250 \cancel {0}}{4\cancel{0} }[/tex]
[tex] \sf \implies\: Length= \cancel\frac{250}{4}[/tex]
[tex] \sf \implies\: Length= \frac{125}{2}[/tex]
[tex]\sf \implies\: Length= 62.5\:cm[/tex]
[tex]\qquad{\rule{200pt}{2pt}}[/tex]
☼︎ Perimeter of Rectangle;
Using Formula:
[tex]\red\bigstar \: {\underline{\boxed{\color{blue}{\textsf{ \textbf{Perimeter of Rectangle = 2(L+B)}}}}}}[/tex]
[tex]\sf \implies\: Perimeter = 2(L+B)[/tex]
[tex]\sf \implies\: Perimeter = 2(62.5+40)[/tex]
[tex]\sf \implies\: Perimeter = 2(102.5)[/tex]
[tex]\sf \implies\: Perimeter of = 2×102.5[/tex]
[tex]\sf \implies\: Perimeter = 2(102.5)[/tex]
[tex]\sf \implies\: Perimeter = 205 \:cm[/tex]
[tex]\qquad{\rule{200pt}{2pt}}[/tex]
Therefore, Length of the rectangle is 62.5 cm and perimeter of the rectangle is 205 cm.