Question

The perimeter of a rectangle is 240cm.
If it's length is decreased by 10% and breadth is increased by 20% we get the same perimeter.Find the original length and breadth of the rectangle

Answer 1

$\huge\mathfrak{\red{Answer}}$

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⇒$\large{\sf{\green{given\:-}}}$

• perimeter of rectangle = 240 cm

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⇒ $\large{\sf{\green{Considering\:-}}}$

• Length = L

• Breath = B

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⇒ $\large{\sf{\green{Solution\:-}}}$

• perimeter of rectangle = 2 ( L + B )

• 240 cm = 2 ( L + B )

• 120 cm = L + B

• L + B = 120 cm

$\large{\sf{\boxed{\red{Equation\:1\:-\:L+B\:=\:120cm}}}}$

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According to question ,

➜ length is decreased by 10%

so, new length of rectangle -

• L = 10 % of length

• L - $\large{\frac{L}{10}}$

• = 0.9 L

➜ Breath of rectangle is increased 20%

so, breath of rectangle -

• B + 20%

• B = B + $\large{\frac{20B}{100}}$

• 1.2 B

➜ now , new perimeter of rectangle =

• 2 ( 0.9L + 1.2B)

➜ but , according to question ,

• initial perimeter = final perimeter

➜ So ,

• 240 = 2 ( 0.9L + 1.2B )

• 0.9L + 1.2B = 120

$\large{\sf{\boxed{\red{Equation2\:-0.9L+1.2B\:=\:120}}}}$

➜ from equation (1) and (2) , multiply 5 with equation (2) and 6 with equation (1)

• 5 ( 0.9L + 1.2B ) - 6 ( L + B ) =

• 5 × 120 - 6 × 120

• 4.5 L - 6 L = - 120

• - 1.5 L = - 120

• L = 80 m

• B = 120 - L = 40 m

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hence ,

LENGTH = $\large{\sf{\boxed{\red{80m}}}}$

BREATH = $\large{\sf{\boxed{\red{40m}}}}$

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