Question

if the perimeter of a rectangle is 120m. and breadth is 18.25m find length

Answer 1

★ᏀᏆᐯᗴᑎ:-

• $\text{Perimeter of rectangle = 120m}$
• $\text{Breadth of rectangle = 18.25m}$

★ᴛᴏ ғɪɴᴅ:-

• $\text{Length of rectangle.}$

★sᴏʟᴜᴛɪᴏɴ:-

$\sf We \: know \: that,$

$\boxed{ \sf Perimeter \: of \: rectangle = 2(Length+Breadth)}$

Using this formula,

$\sf \leadsto 120m = 2(Length + 18.25m)$

$\sf \leadsto 120m = 2Length + 36.5m$

$\sf \leadsto 2Length = 120m - 36.5m$

$\sf \leadsto 2Length = 83.5m$

$\sf \leadsto Length = 10 \Bigg (\dfrac{83.5m}{2} \Bigg ) = \dfrac{835m}{20} = 41.75m$

I multiplied the fraction by 10 so that the decimal goes away.

$\boxed{\bold {Length \: of \: the \: rectangle= 41.75m}}$

Answer 2

$\green{\large\underline{\underline\mathtt{Question:}}}$

If the perimeter of a rectangle is 120 m , and breadth is 18.25 m then find its length.

$\orange{\large\underline{\underline\mathtt{To\:Find:}}}$

• To finds it's length:-

$\purple{\large\underline{\underline\mathtt{Given:}}}$

• $\mathtt{Perimeter = 120 m}$
• $\mathtt{Breadth = 18.25 m}$

$\red{\large\underline{\underline\mathtt{Taken:}}}$

→ Let the Length be l m.

$\green{\large\underline{\underline\mathtt{We\:know:}}}$

$\underline{\boxed{\mathtt{Perimeter = 2(length + breadth)}}}$

$\blue{\large\underline{\underline\mathtt{Concept:}}}$

By using the formula for perimeter of a reactangle , we can find the formula for length of the rectangle.i.e,

$Perimeter = 2(length + Breadth)$

$\therefore length = \dfrac{perimeter}{2} - breadth$

$\purple{\large\underline{\underline\mathtt{Solution:}}}$

We know,

$length = \dfrac{perimeter}{2} - breadth$

Putting the value in the formula , we get:-

$\Rightarrow l = \dfrac{120}{2} - 18.25$

$\Rightarrow l = \dfrac{120 - 36.50}{2}$

$\Rightarrow l = \dfrac{83.5}{2}$

$\Rightarrow l = \dfrac{\cancel{83.5}}{\cancel{2}}$

$\Rightarrow l = 41.75 m$

$\therefore Length \rightarrow l = 41.75 m$

$\red{\large\underline{\underline\mathtt{Verification:}}}$

We know,

$Perimeter = 2(length + Breadth)$

Putting the value the equation , we get

• length = 41.75 m
• Breadth = 18.25 m
• perimeter = 120 m

$\Rightarrow 120 = 2(41.75 + 18.25)$

$\Rightarrow 120 = 2(60)$

$\Rightarrow 120 = 120$

$\therefore LHS = RHS$

Hence, the value of Length is correct :)

$\blue{\large\underline{\underline\mathtt{Extra\: information:}}}$

• $Breadth = \dfrac{perimeter}{2} - length$
• $Area(rectangle) = length \times breadth$
• $Area(square) = side \times side$

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