Question

The area of a square field is
256 m² whose perimeter
is equal to the perimeter of a rectanglear field
whose length is thrice it's breath find the dimension
of the rectangular field​

Answer 1

Answer:

☆$\large{\boxed{\green{\mathcal{Answer-}}}}$☆

GIVEN :

AREA OF SQUARE = 256 M. SQ.

THE PERIMETER OF SQUARE = PERIMETER OF RECTANGLE .

LENGTH OF RECTANGLE = 3 BREADTH OF THE RECTANGLE.

TO FIND :

DIMENSIONS OF RECTANGLE

PROOF :

LET THE BREADTH OF THE RECTANGLE BE X .

ACCORDING TO THE CONDITIONS ;

L = 2X

B = X

$area \: = side \times side \\ 256 = {side }^{2} \\ side \: = \sqrt{256 } \\ side = 16m$

GIVEN THAT THE PERIMETER OF THE RECTANGLE IS SAME AS THE PERIMETER OF THE SQUARE ,

THEREFORE ,

PERIMETER OF SQUARE = 4 (16)

= 64 M

PERIMETER OF RECTANGLE = 2 (L + B)

= 2 (3X + X)

= 2(4X)

PERIMETER OF RECTANGLE = 8X

THEREFORE ;

8X = 64

X = 64 / 8

X = 32/4

X = 8 M

THEREFORE ;

BREADTH = X

= 8M

LENGTH = 3X

= 3 × 8

= 24 M

♡LENGTH = 24 M AND BREADTH = 8 M ♧

Answer 2

Step-by-step explanation:

$\huge \mathcal \red{A}\huge \mathcal \green{n}\huge \mathcal\orange{S}\huge \mathcal\blue{w}\huge \mathcal{E}\huge \mathcal\orange{r-}$

$\bold{Given - } \\ Area \: o f \: a \: square = \bold{256 \: {m}^{2}} \\ \\ (side) {}^{2} = 256 {m}^{2} \\ \\ As \: we \: know \: that \: all \: \bold{sides \: of \: square} \: are \: \bold{equal} \\ then, \\ \\ let \: x \: be \: the \: side \: of \: square \\ \\ {x}^{2} = 256 \\ \\ x = \sqrt{256} \\ \\ x = 16 \: m \\ \\ \fbox \bold{side = 16 \: m} \\ \\ \bold{Given - } \\ \\ \bold{Perimeter \: of \: Square = Perimeter \: of \: \: Rectangle} \\ \\ Perimeter \: of \: square = \bold{4 \times side}</p><p> \\ \\ </p><p>side = \bold{16 m}</p><p> \\ \\ </p><p>Perimeter of square = 4 \times 16</p><p> \\ \\ </p><p>= \bold{64 m}</p><p>$

$64 = 2(l + b) \\ \\l + b = 32 \\ \\ \bold{Given - } \\ \\ \bold{Length \: is \: thrice \: times \: its \: breadth} \\ \\ let \: the \: Breadth \: be \: \bold{x} \\ \\ then \: Length = \bold{3x} \\ \\ 3x + x = 32 \\ \\ 4x = 32 \\ \\ x = \frac{32}{4} \\ \\ x = \bold{8 \: m} \\ \\ then \\ \\ Length = 3x = 3 \times 8 = \bold{24 \: m \: } \\ \\ and \\ \\ Breadth = x = \bold {8 \: m}$