Question

The length of a rectangle is twice that of its breadth. If the length of the rectangle is increased by 20% while its breadth is decreased by 20%, determine the percentage change, if any, in its perimeter.
If anyone answers correctly with proper explain, then I will mark as brainliest​

Answer 1

Step-by-step explanation:

breadth=x

⇒ Length=2x

⇒ Area of rectangle=2x×x

=2x

2

After the given changes;

length=2x−5

Breadth=x+5

Area=2x

2

+75

⇒(2x−5)(x+5)=2x

2

+75

2x

2

−5x+10x−25=2x

2

+75

5x=75+25=100

⇒x=20

⇒ Breadth=20cm

Length=40cm.

Answer 2

$\large{\underline{\red{\bf{Question:-}}}}$

• The length of a rectangle is twice that of its breadth. If the length of the rectangle is increased by 20% while its breadth is decreased by 20%, determine the percentage change, if any, in its perimeter.

$\large{\underline{\purple{\bf{Solution:-}}}}$

➢ Let the breadth of the rectangle be 100 .Then,

➢ Length of the rectangle be (2 × 100) = 200.

⋆ Original Perimeter of Rectangle :- 2(L + B)

➛ 2(L + B)

➛ 2(200 + 100)

➛ 2(300)

➛ 600 unit

Now, According to the Question:-

➢ New length of rectangle :-

$➛ \:\frac{120}{100} \times 100 \\ \\ ➛120 \: \: unit$

➢ New Breadth of the Rectangle:-

$➛ \frac{80}{100} \times 200 \\ \\ ➛160 \: unit$

⋆ New Perimeter of the rectangle:-

➛ 2(L + B)

➛ 2(120 + 160)

➛ 2(280)

➛ 560 unit

✰ Change in both Perimeters:-

$➝ Change (\%) = \frac{(Original-New)}{Original} × 100 \\ \\ ➝ \: Change (\%) = \frac{(600 - 560)}{600} \times 100 \\ \\ ➝ \: Change (\%) = \frac{40}{6} \\ \\ ➝ \: Change (\%) = 6.67\% \\ \\ ➝ \: Change (\%) = 6 \: \frac{4}{6} \%$

$\fbox \purple{\:★ Change Percentage in Perimeters is 6.67 \: \% }$