Question

length of rectangular ground is 3 more then it's breadth. perimeter of ground is 76. find the dimensions​

Answer 1

Dimensions :-

• Length is 20.5 .
• Breadth is 17.5 .

Step-by-step explanation:

Given:-

• Perimeter of ground is 76.

To find:-

• Dimensions of ground.

Solution:-

Let, Breadth of rectangular ground be x.

And, Length of rectangular ground be x + 3 [We take length be x + 3 because it is given that length is 3 more than Breadth]

We know,

Perimeter of rectangle = 2(l + b)

Where,

• l is length and b is breadth

Put the values:

$\longrightarrow$ 76 = 2 × (x + 3 + x)

$\longrightarrow$ 76 = 2x + 6 + 2x

$\longrightarrow$ 76 = 4x + 6

$\longrightarrow$ 76 - 6 = 4x

$\longrightarrow$ 70 = 4x

$\longrightarrow$ x = 70/4

$\longrightarrow$ x = 17.5

Verification:-

$\longrightarrow$ 76 = 2×(x + 3 + x)

• Put x = 17.5

$\longrightarrow$ 76 = 2×(17.5 + 3 + 17.5)

$\longrightarrow$ 76 = 2×(20.5 + 17.5)

$\longrightarrow$ 76 = 41 + 35

$\longrightarrow$ 76 = 76

$\boxed{\sf Hence \: Verified.}$

Dimensions are:

We take

Breadth be x . So, Breadth of rectangular ground is 17.5 .

Length be x + 3 = 17.5 + 3 = 20.5. Thus, Length of rectangular ground is 20.5 .

Answer 2

$\Huge \rm \fbox{Correct Question}$

$\sf{Length \: of \: rectangular \: ground \: is \: 3 \: more \: then}$

$\sf{its \: breadth.If \: perimeter \: of \: ground \: is \: 76cm, find}$

$\sf{its \: dimensions.}$

$\Huge \rm \fbox{Answer}$

$\Large \bf{Given:}$

$\sf\implies{Breadth \: of \: rectangle= {\bf{x}} \: cm}$

$\sf\implies{Length \: of \: rectangle=3 + {\bf{x}} cm}$

$\sf\implies{Perimeter \: of \: rectangle=76 {cm} }$

$\Large \bf{To \: find:}$

$\leadsto \sf{Dimension \: of \: rectangle. }$

$\Large \bf{Formula \: required:}$

$\fbox{Perimeter of rectangle=2(length+breadth)}$

$\Large \bf{According \: to \: Question:}$

$\sf \mapsto{Perimeter \: of \: rectangle=2(length+breadth)}$

$\sf \mapsto{76 {cm} =2(3 + {\bf{x}}+ \bf{x})}$

$\sf \mapsto{ \frac{76}{2} =3 + 2 {\bf{x}}}$

$\sf \mapsto{ 38 =3 + 2 {\bf{x}}}$

$\sf \mapsto{ {38} - {3} = 2{\bf{x}}}$

$\sf \mapsto{ 35 = 2{\bf{x}}}$

$\sf \mapsto{ \frac{35}{2} = {\bf{x}}}$

$\sf \mapsto{ 17.5 = {\bf{x}}}$

$\sf{ \longrightarrow{Breadth \: of \: rectangle=17.5cm}}$

$\sf{ \longrightarrow{Length \: of \: rectangle=17.5cm + 3 = 20.5cm}}$

$\Large \bf{Verification:}$

$\sf \mapsto{Perimeter \: of \: rectangle=2(length+breadth)}$

$\sf \mapsto{76cm=2(20.5+17.5)}$

$\sf \mapsto{76cm=2 \times 38.0}$

$\sf \mapsto{76cm=76cm}$

$\fbox{L.H.S=R.H.S}$

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