Question

10. The length of a ractangular field is 8 meters less than twice its breadth. If the
perimeter of the rectangular field is 56 meters. Find its lengh and breadth​

Answer 1

Given :

• The length of a rectangular field is 8 meters less than twice its breadth.
• Perimeter of the rectangle = 56 meters.

To find :

• Length of the rectangular field = ?
• Breadth of the rectangular field = ?

Solution :

Let the breadth of the rectangular field be ‘x’ m.

So, length will be (2x - 8) m.

Given, perimeter of a rectangular field = 56 m.

We know that,

$\qquad \red {\underline {\boxed {\sf Perimeter \ = \ 2(l + b)}}}$

$\implies \sf 2(l + b) \ = \ 56$

$\implies \sf l + b \ = \ \dfrac {56}{2}$

$\implies \sf l + b \ = \ 28$

$\implies \sf x + 2x - 8 \ = \ 28$

$\implies \sf 3 x \ = \ 36$

$\implies \sf x \ = \ \dfrac {36}{3}$

$\qquad \red {\underline {\boxed {\therefore \sf x \ = \ 12 \ m}}}$

Now,

Length of the rectangular field = ?

$\implies \sf length \ = \ 2x - 8$

$\implies \sf length = 2 \times 12 - 8$

$\qquad \red {\underline {\boxed {\sf Length \ = \ 16 \ m}}}$

$\therefore$ The length of the rectangular field is 16 m.

$\therefore$ The breadth of the rectangular field is 12 m.

Answer 2

$\: \:{\large{\bold{\sf{\underbrace{Understanding \: the \: question}}}}}$

➥ This question says that there is a rectangular field it's length is 8 metres less than twice it's breadth. Now this question says that the perimeter of that rectangular field is 56 m. And at last we have to find its length and breadth.

$\: \:{\large{\bold{\sf{\underbrace{Given \: that}}}}}$

➦ Perimeter of rectangular field = 56 m

➦ The length of rectangular field is 8 metres less than twice it's breadth.

$\: \:{\large{\bold{\sf{\underbrace{To \: find}}}}}$

➦ Length of rectangular field

➦ Breadth of rectangular field

$\: \:{\large{\bold{\sf{\underbrace{Solution}}}}}$

➦ Length of rectangular field = 16 m

➦ Breadth of rectangular field = 12 m

$\setlength{\unitlength}{1cm}\begin{picture}(0,0)\thicklines\multiput(0,0)(5,0){2}{\line(0,1){3}}\multiput(0,0)(0,3){2}{\line(1,0){5}}\put(0.03,0.02){\framebox(0.25,0.25)}\put(0.03,2.75){\framebox(0.25,0.25)}\put(4.74,2.75){\framebox(0.25,0.25)}\put(4.74,0.02){\framebox(0.25,0.25)}\multiput(2.1,-0.7)(0,4.2){2}{\sf\large 16 m}\multiput(-1.4,1.4)(6.8,0){2}{\sf\large 12 m}\put(-0.5,-0.4){\bf A}\put(-0.5,3.2){\bf D}\put(5.3,-0.4){\bf B}\put(5.3,3.2){\bf C}\end{picture}$

$\: \:{\large{\bold{\sf{\underbrace{Using \: concepts}}}}}$

➥ Perimeter of rectangle formula.

$\: \:{\large{\bold{\sf{\underbrace{Using \: formulas}}}}}$

➥ Perimeter of rectangle = 2(l+b)

$\: \:{\large{\bold{\sf{\underbrace{We \: also \: write \: these \: as}}}}}$

➥ Length as l

➥ Breadth as b

➥ Perimeter as p

$\: \:{\large{\bold{\sf{\underbrace{Full \: solution}}}}}$

➨ According to the question the length will be (2b - 8) metres. Here, b denotes breadth.

~ Finding breadth of this rectangular field

➻ Perimeter of rectangle = 2(l+b)

➻ 56 = 2(2b-8 + b)

➻ 56 = 4b - 16 + 2b

➻ 56 = 4b + 2b - 16

➻ 56 = 6b - 16

➻ 56 + 16 = 6b

➻ 72 = 6b

➻ 72/6 = b

➻ 36/3 = b

➻ 12 = b

➻ b = 12 metres

• Henceforth, the value of b is 12 m means the measurement of breadth is 12 metres.

~ Finding length of this rectangular field

➻ l = 2b - 8

➻ l = 2(12) - 8

➻ l = 2 × 12 - 8

➻ l = 24 - 8

➻ l = 16 metres

• Henceforth, the value of l is 16 m means the measurement of length is 16 metres.

$\: \:{\large{\bold{\sf{\underbrace{Knowledge}}}}}$

Diagram of a rectangle –

$\setlength{\unitlength}{1cm}\begin{picture}(0,0)\thicklines\multiput(0,0)(5,0){2}{\line(0,1){3}}\multiput(0,0)(0,3){2}{\line(1,0){5}}\put(0.03,0.02){\framebox(0.25,0.25)}\put(0.03,2.75){\framebox(0.25,0.25)}\put(4.74,2.75){\framebox(0.25,0.25)}\put(4.74,0.02){\framebox(0.25,0.25)}\multiput(2.1,-0.7)(0,4.2){2}{\sf\large x cm}\multiput(-1.4,1.4)(6.8,0){2}{\sf\large y cm}\put(-0.5,-0.4){\bf A}\put(-0.5,3.2){\bf D}\put(5.3,-0.4){\bf B}\put(5.3,3.2){\bf C}\end{picture}$

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