Question

perimeter of rectangle is 180 metre and its length is 10 metre more than its width find the length and with the answer NCERT solution​

Answer 1

$\sf\red{\underline{\underline{Answer:}}}$

$\sf{The \ length \ and \ width \ of \ rectangle \ are}$

$\sf{50 \ cm \ and \ 40 \ cm \ respectively. }$

$\sf\orange{Given:}$

$\sf{\longmapsto{Perimeter \ of \ rectangle=180 \ m}}$

$\sf{\longmapsto{Length \ is \ 10 \ meter \ more \ than | width.}}$

$\sf\pink{To \ find:}$

$\sf{Width \ of \ the \ rectangle. }$

$\sf\green{\underline{\underline{Solution:}}}$

$\sf{Let \ the \ width \ of \ the \ rectangle \ be \ x \ cm}$

$\sf{By \ the \ given \ condition}$

$\sf{Length=x+10}$

$\sf{Here,}$

$\sf{\leadsto{Length(l)=x+10,}}$

$\sf{\leadsto{Breadth(b)=x}}$

$\boxed{\sf{Perimeter \ of \ rectangle=2(l+b)}}$

$\sf{\therefore{180=2(x+x+10)}}$

$\sf{\therefore{\dfrac{180}{2}=2x+10}}$

$\sf{\therefore{2x+10=90}}$

$\sf{\therefore{2x=90-10}}$

$\sf{\therefore{2x=80}}$

$\sf{\therefore{x=\dfrac{80}{2}}}$

$\sf{\therefore{x=40}}$

$\sf{\leadsto{Width=x=40 \ cm,}}$

$\sf{\leadsto{Length=x+10=50 \ cm}}$

$\sf\purple{\tt{\therefore{The \ length \ and \ width \ of \ rectangle \ are}}}$

$\sf\purple{\tt{50 \ cm \ and \ 40 \ cm \ respectively. }}$

______________________________________

$\sf\blue{\underline{\underline{Extra \ information:}}}$

$\sf{\leadsto{Area=l\times \ b}}$

Answer 2

$\large\bf\underline {To \: find:-}$

• we need to find the length of rectangle.

$\huge\bf\underline{Solution:-}$

$\bf\underline{\red{Given:-}}$

• Perimeter of rectangle = 180m
• length of rectangle is 10m more than it's width.

Let the width of rectangle be x meter .

so ,

Length of rectangle is (x + 3) meters

we know that,

▶ perimeter of rectangle is 2 ×(l + b)

→ 2 × (x + x +10) = 180

→ 2 × (2x + 10) = 180

→ 2x + 10 = 180/2

→ 2x + 10 = 90

→ 2x = 90 - 10

→ 2x = 80

→ x = 80/2

→ x = 40m

Hence,

Width of rectangle x = 40m

Length of rectangle x + 3 = 40 + 10 = 50m

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⠀⠀⠀༒Some formulas :-

⪼ Area of rectangle = l × b

⪼ Perimeter of rectangle = 2(l + b)

⪼ Length of rectangle = Area/Breadth

⪼ Breadth of rectangle = Area/length

⪼ Diagonal of rectangle = √l² + b²

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