Question

if the perimeter of rectangle is 434cm and it's adjacent side are in ratio 5:2.fimd the length of all side​

Answer 1

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

• Perimeter of rectangle = 434 cm
• Ratio of sides of rectangle = 5:2

$\rm{ \underline{ \huge{To \: \: find: }}}$

• Length of sides of rectangle

$\rm{ \underline{ \huge{Solution: }}}$

Put x in the ratio,

• Length of rectangle = 5x
• Breadth of rectangle = 2x

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \mathfrak{ \green{ \underline{ \large{Formula \: to \: calculate \: the \: perimeter \: of \: rectangle \: \: }}}}$

$\boxed{ \mathfrak{ \red{ \large{ perimeter = 2(length + breadth)}}}}$

According to question,

$\large{ \tt \implies \: \: \: \: \: \: \: \: \: 2(5x + 2x) = 434}$

$\large{ \tt \implies \: \: \: \: \: \: \: \: \: 2(7x) = 434}$

$\large{ \tt \implies \: \: \: \: \: \: \: \: \: 7x = \frac{434}{2} }$

$\large{ \tt \implies \: \: \: \: \: \: \: \: \: 7x = 217}$

$\large{ \tt \implies \: \: \: \: \: \: \: \: \: x = \frac{217}{7} }$

$\large{ \tt \implies \: \: \: \: \: \: \: \: \: x = 31}$

Now,

• Length of rectangle = 5x = 155 cm
• Breadth of rectangle = 2x = 62 cm

$\rm{ \underline{ \huge{ Hence:}}}$

The sides of rectangle are 155 cm and 62 cm

Answer 2

$\:\:\:\: \large \underline {\sf{Given\::}}$

➟ The perimeter of rectangle is 434 cm and it's adjacent side are in ratio 5:2

$\:\:\:\: \large \underline {\sf{To\:Find\::}}$

➟ Length and Breadth

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

• Let the unknown value be x

Here , Length = 5x and Breadth = 2x

$\:\:\:\: \star \large \underline {\sf{Formula\:used\:: }}$

$\:\:\:\:\:\: \large {\boxed{\boxed{\sf{\pink{Perimeter\:=\:2(l\:+\:b)}}}}}$

➟ 434 = 2(5x + 2x)

➟ 434 = 10x + 4x

➟ 434 = 14x

➟ x = 434/14

➟ x = 31 cm

• Length = 5x = 5(31) = 155 cm
• Breadth = 2x = 2(31) = 62 cm

ᶠⁱⁿᵃˡ ᵃⁿˢ ⁱˢ 155 ᶜᵐ ᵃⁿᵈ 62 ᶜᵐ ʳᵉˢᵖᵉᶜᵗⁱᵛᵉˡʸ

ᵃⁿᵈ ʷᵉ ᵃʳᵉ ᵈᵒⁿᵉ !

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