Question

8. The length of a rectangular field is 5
times its breadth. If the perimeter of
the field is 108 m, find its length and
breadth​

Answer 1

⛦ Given :

• Length of rectangle is 5 times it's breadth.
• Perimeter of rectangle = 108 m

⛦ To find :

• The Length.
• And the Breadth.

⛦ Solution :

Firstly, let's assume the Breadth be x

Then , the Length = 5x

✯Perimeter of rectangle = 2( l + b)

Where, L = length and B = breadth

According to Question ,

⇢108 = 2(5x + x)

⇢108 = 10x + 2x

⇢108 = 12x

⇢108/12 = x

⇢9 = x

✭ x = 9 ✭

Therefore,

• The Breadth = 9m
• And Length = 5x = 5×9 = 45

_____________

Let's verify our answer !

✯Perimeter of rectangle = 2(l + b)

⟿ 108 = 2 (45 + 9)

⟿ 108 = 2 × 54

⟿ 108 = 108

Therefore,the length(l) and Breadth (b) are correct.

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Answer 2

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

$\sf \underline{length = 45m}$

$\sf \underline{breadth = 9m}$

$\sf \huge \underline \pink{Given : }$

• The length of a rectangular field is 5 times its breadth

• If the perimeter of the field is 108m

$\sf \huge \underline \green{To \: find : }$

• length and breadth

$\sf \huge \underline \orange{solution : }$

$\sf \underline{ let \: the \: breadth \: be \: x}$

$\sf \underline{ length \: be \: 5x}$

$\sf \underline{perimeter \: is \: 108m}$

$\: \: \: \sf \underline{we \: know \: that \: perimeter \: formula : }$

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \bf{ \boxed{ \underline{ \underline{ \red{ \tt{2( {l} + {b}) \: }}}}}}$

$\: \: \: \: \: \: \: \: \: \: \: \: \: \sf{ \implies \: 2(x + 5x) = 108}$

$\: \: \: \: \: \: \: \: \: \: \: \: \: \sf{ \implies \: x + 5x = \dfrac{108}{2} }$

$\: \: \: \: \: \: \: \: \: \: \: \: \: \sf{ \implies \: 6x = 54m}$

$\: \: \: \: \: \: \: \: \: \: \: \: \: \sf{ \implies \: x = \dfrac{54}{6} }$

$\: \: \: \: \: \: \: \: \: \: \: \: \: \sf{ \implies \: x = 9}$

$\: \: \: \: \: \: \: \: \: \: \: \: \: \sf{ breadth = 9m}$

$\: \: \: \: \: \: \: \: \: \: \: \: \: \sf{ length = 5 \times 9 = 45m}$