Question

Perimeter of a rectangle is equal to the perimeter of square whose area is 400 cm^2.Find the area of rectangle if length of rectangle is 40% more than the side of square​

Answer 1

Answer:

Perimeter= 82

2*(l+b)=82 => l+b=41 —(1)

Area=400 m^2

l*b=400 —(2)

Replacing equation (1) in equation (2), we get

(41-b)*b=400 => 41b-b^2=400 => b^2–41b+400=0

Solving this, we get b=25,16

Corresponding l=16,25

As we know breadth is smaller than length, hence breadth = 16

Answer 2

Answer :-

• The area of the rectangle is 336 cm².

To find :-

• The area of the rectangle.

Step-by-step explanation :-

• Here, we have to find the area of the rectangle. For that, we will have to find out it's dimensions first!

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Let's find the side of the square first!

We know that :-

$\underline{\boxed{\sf Area \: of\: a \:square = Side^2}}$

Here,

• Area = 400 cm².

• Let the side be "s".

Substituting the given values in this formula,

$\rm 400 = s^2$

To find the side of the square, we have to find the square root of 400.

$\rm \sqrt{400} = s$

Finding the square root of 400,

$\overline{\boxed{\rm 20 \: cm = s}}$

Now, as we know the side of the square, let's find it's perimeter!

We know that :-

$\underline{\boxed{\sf Perimeter \: of\: a \: square = 4 \times Side}}$

Here,

• Side = 20 cm.

Hence,

$\rm Perimeter = 4 \times 20$

Multiplying 4 with 20,

$\overline{\boxed{\rm Perimeter = 80 \: cm}}$

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Now, it has been given that :-

• The perimeter of the rectangle is equal to the perimeter of the square.

• Here, perimeter of the square is 80 cm, which means that the perimeter of the rectangle is 80 cm too.

It has also been given that :-

• The length of the rectangle is 40% more than the side of the square.

• The side of the square is 20 cm, which means that the length of the rectangle is 40% more than 20 cm.

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Let's find out 40% of 20 cm first!

$\tt 40\% \: of \: 20$

Converting 40% into fraction,

$\tt \dfrac{40}{100} \times 20$

Cutting off the zeroes,

$\tt \dfrac{4}{1} \times 2$

Now let's multiply the remaining numbers since we can't reduce them anymore.

$\tt 4\times2$

Multiplying the numbers,

$\overline{\boxed{\tt 8}}$

Now let's find the length of the rectangle!

• 40% of 20 cm is 8 cm.

Hence,

• The length of the rectangle = 20 + 8 = 28 cm.

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As we know the length now, let's find the breadth of the rectangle!

We know that :-

$\underline{\boxed{\sf Perimeter \: of \: a \: rectangle = 2 \: (L + B)}}$

Where,

• L = Length.
• B = Breadth.

Here,

• Length = 28 cm.
• Perimeter = 80 cm.

• Let the breadth be "b".

Substituting the given values in this formula,

$\rm 80 = 2 \: (28 + b)$

Removing the brackets,

$\rm 80 = 56 + 2b$

Transposing 56 from RHS to LHS, changing it's sign,

$\rm 80 - 56 = 2b$

Subtracting 56 from 80,

$\rm 24 = 2b$

Transposing 2 from RHS to LHS, changing it's sign,

$\rm \dfrac{24}{2} = b$

Dividing 24 by 2,

$\overline{\boxed{\rm 12 \: cm= b}}$

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Finally, let's find the area of the rectangle!

We know that :-

$\underline{\boxed{\sf Area \: of \: a \: rectangle = L \times B}}$

Where,

• L = Length.
• B = Breadth.

Here,

• Length = 28 cm.
• Breadth = 12 cm.

Hence,

$\tt Area = 28 \times 12$

Multiplying 28 with 12,

$\overline{\boxed{\tt Area = 336 \: cm^2}}$

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• Therefore, the area of the rectangle is 336 cm².