Question

The area of a square plot is 5184m^2.A rectangular field,whose length is twice its breadth,has its perimeter equal to the perimeter of the square field.Find the area of the rectangular field.​

Answer 1

Answer:

Given:-

The area of a square plot is 5184m². A rectangular field whose length is twice its breadth, has its perimeter equal to the perimeter of the square field. Find the area of the rectangular field.

To Find:-

The area of rectangular field.

Note:-

●》Here; we will first find the "side of a square" for calculating "perimeter of square" field for finding "perimeter of rectangular field" ( Perimeter of square field = Perimeter of rectangular field ) because from the "perimeter of rectangle", we can find "length" and "breadth" from which "area of rectangular field will be calculated".

□ Side of a square = √Area of square plot.

□ Perimeter of square field = 4 × Side.

□ Perimeter of rectangular field = 2 × ( Length + Breadth ).

□ Area of rectangular field = Length × Breadth.

●》Transposing is also required during solution i.e. Transposing is a process in which we change the side of known value to find unknown value and also in this process numbers signs are changed. For example - Multiple becomes Divisional.

Solution:-

[ So, first finding side of square ]

$\huge\red{Area \ \ of \ \ square \ \ plot = 5184m²}$

$\huge\red{It's \ \ side = ?}$

☆ According to note first point ( First box )~

▪︎$Side \ \ of \ \ a \ \ square = \sqrt Area \ \ of \ \ square \ \ plot$

▪︎$Side \ \ of \ \ a \ \ square = \sqrt 5184m²$

▪︎$Side \ \ of \ \ a \ \ square = \sqrt 72m × 72m$

▪︎$Side \ \ of \ \ a \ \ square = 72m$

$\huge\pink{It's \ \ side = 72m}$

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[ Now, we will find perimeter of square field ]

$\huge\red{Side \ \ of \ \ a \ \ square = 72m}$

$\huge\red{Perimeter \ \ of \ \ square = ?}$

☆ According to note first point only ( Second box )~

▪︎$Perimeter \ \ of \ \ a \ \ square = 4 × Side$

▪︎$Perimeter \ \ of \ \ a \ \ square = 4 × 72m$

▪︎$Perimeter \ \ of \ \ a \ \ square = 288m$

$\huge\pink{Perimeter \ \ of \ \ a \ \ square = 288m}$

_______________________________________________

[ Now, perimeter of rectangular field ]

$\huge\red{Perimeter \ \ of \ \ square \ \ field = 288m}$

$\huge\red{Perimeter \ \ of \ \ rectangular \ \ field = ?}$

☆ As we know~

▪︎$Perimeter \ \ of \ \ square = Perimeter \ \ of \ \ rectangular \ \ field$

▪︎$288m = 288m$

$\huge\pink{Perimeter \ \ of \ \ rectangular \ \ field = 288m}$

_______________________________________________

[ Now, we will find length and breadth ]

$\huge\red{Perimeter \ \ of \ \ rectangular \ \ field = 288m}$

$\huge\red{Breadth = ?, Let \ \ it \ \ be = x}$

$\huge\red{So, Length \ \ will \ \ be = 2x}$

☆ According to note first point only ( Third box )~

▪︎$Perimeter \ \ of \ \ rectangular \ \ field = 2 × ( Length + Breadth )$

▪︎$288m = 2 × ( 2x + x )$

▪︎$288m = 2 × ( 3x )$

▪︎$288m = 6x$

☆ According to note second point ( Transposing )~

▪︎$\dfrac{288m}{6} = x$

▪︎$\cancel\dfrac{288m}{6} = x$

▪︎$48m = x$

$\huge\pink{So, Breadth = x => 48m}$

$\huge\pink{Length = 2x = 2 × 48m => 96m}$

______________________________________________

[ Now, we will find area of rectangular field ]

$\huge\red{Length = 96m, Breadth = 48m}$

$\huge\red{ \ \ \ \ Area \ \ of \ \ rectangular \ \ field = ?}$

☆ According to note first point only ( Fourth box )~

▪︎$Area \ \ of \ \ rectangular \ \ field = Length × Breadth$

▪︎$Area \ \ of \ \ rectangular \ \ field = 96m × 48m$

☆ After multiplying~

▪︎$Area \ \ of \ \ rectangular \ \ field = 4,608m²$

$\huge\green{Area \ \ of \ \ rectangular \ \ field = 4,608m²}$

Answer:-

Hence, The area of rectangular field = 4,608m².

:)