Question

Find the breadth of a rectangle whose length is double of its breadth and perimeter is 720m.

Answer 1

Given : The length is double of its breadth and perimeter is 720 m .

Need To Find : Breadth of Rectangle.

⠀⠀⠀⠀⠀⠀⠀⠀━━━━━━━━━━━━━━━━━━━⠀⠀⠀⠀

⠀⠀⠀⠀❍ Let's consider the Breadth of Rectangle be x m

⠀⠀⠀⠀

Given that ,

⠀⠀⠀⠀The length is double of its breadth .

⠀⠀⠀⠀⠀⠀$\therefore$ The Length of Rectangle is 2x m .

⠀⠀⠀⠀

⠀⠀⠀$\frak{\underline {As\:We\:know\:that\::}}$

⠀⠀⠀⠀⠀ $\pink {\boxed {\sf{ Perimeter _{(Rectangle)} = 2 ( l + b ) \: .}}}$

⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀Here l is the Length of Rectangle in metres and b is the Breadth of Rectangle in metres and we have given with the Perimeter of Rectangle is 720 m .

⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀$\underline {\frak{\star\:Now \: By \: Substituting \: the \: Given \: Values \::}}$

⠀⠀⠀⠀

⠀⠀⠀⠀$:\implies {\mathrm {720m  = 2( x + 2x )   }}$

⠀⠀⠀⠀⠀⠀⠀$:\implies {\mathrm { \dfrac{720}{2} = x + 2x   }}$

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀$:\implies {\mathrm {360  = x + 2x   }}$

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀$:\implies {\mathrm {360  = 3x   }}$

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀$:\implies {\mathrm { \dfrac{360}{3}  = x   }}$

⠀⠀⠀⠀⠀⠀⠀⠀$\underline {\boxed{\pink{ \mathrm {  x = 120 \: m}}}}\bf{\bigstar}$

⠀⠀⠀⠀

Therefore,

• Length of Rectangle is 2x = 2 × 120 = 240 m

• Breadth of Rectangle is x = 120 m

⠀⠀⠀⠀

⠀⠀⠀⠀⠀$\underline {\therefore\:{\pink{ \mathrm { Breadth \:of\:Rectangle \:is\:120\: m}}}}$

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⠀⠀⠀⠀⠀⠀⠀⠀━━━━━━━━━━━━━━━━━━━⠀⠀⠀⠀

$\qquad\quad\boxed{\bf{\mid{\overline{\underline{\blue{\bigstar\: Verification \: :}}}}}\mid}$

⠀⠀⠀⠀⠀ $\pink {\boxed {\sf{ Perimeter _{(Rectangle)} = 2 ( l + b ) \: .}}}$

⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀Here l is the Length of Rectangle in metres and b is the Breadth of Rectangle in metres and we have given with the Perimeter of Rectangle is 720 m .

⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀$\underline {\bf{\star\:Now \: By \: Substituting \: the \: Found \: Values \:in\:Formula \::}}$

⠀⠀⠀⠀$:\implies {\mathrm {720  m = 2 ( 120 + 240 ) }}$

⠀⠀⠀⠀⠀⠀⠀$:\implies {\mathrm {720 m = 2 ( 360 ) }}$

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀$:\implies {\mathrm {720m  = 720m   }}$

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀$\therefore {\sf{\bf{ Hence \:Verified \:}}}$

⠀⠀⠀⠀⠀⠀⠀⠀━━━━━━━━━━━━━━━━━━━⠀⠀⠀⠀

Answer 2

DIAGRAM :

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$\: \:$

Given : Length of a rectangle is double than it's breadth and it's perimeter is 720m.

To Find : Breadth of the rectangle.

⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀____________________

• Let the breadth of the rectangle = k

$\: \:$

Here, Length of the rectangle is double of it's breadth.

$\: \:$

• So, length of the rectangle = 2k

$\: \:$

Here, value of perimeter of the rectangle is also given as 720m.

$\: \:$

For finding the perimeter of the rectangle, formula is given as :

$\:$

$\star\underline{\boxed{\sf\pink{Perimeter_{(rectangle)} = 2(l + b)}}}$

$\: \:$

Where, l denotes length of the rectangle and b denotes breadth of the rectangle.

⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀____________________

$\: \:$

$\bold{\underline{According \: to \: the \: question \: :}}$

$\:$

$\sf:\implies \: Perimeter_{(rectangle)} = 2(l + b) \\ \\ \\ \sf:\implies \: Perimeter_{(rectangle)} = 2(2k + k) \\ \\ \\ \sf:\implies720 = 2 \times 3k \\ \\ \\ \sf:\implies720 = 6k \\ \\ \\ \sf:\implies \: k = \cancel \frac{720}{6} \\ \\ \\ \sf:\implies\underline{\boxed{\mathfrak\purple{k = 120m}}} \: \bigstar$

$\: \:$

Now,

$\: \:$

• Breadth of the rectangle = k = 120m
• Length of the rectangle = 2k = 2(120) = 240m

$\: \:$

$\: \:$

$\sf\therefore{\underline{Hence, \: the \:breadth \: of \: the \: rectangle \: is \: \bold{120 m}.}}$