Question

The area of a square sheet of paper of side 10 cm is the same as that of a rectangular sheet of length 25cm. what is the perimeter of the rectangle ?

Answer 1

Step-by-step explanation:

Given :-

The area of a square sheet of paper of side 10 cm is the same as that of a rectangular sheet of length 25 cm.

To find :-

The perimeter of the rectangle .

Solution :-

Given that

The side of a square sheet of the paper

(s) = 10 cm

We know that

Area of a square of 's' units is 's²' sq.units

Area of the given square sheet of the paper

=> A = 10² cm²

=> A = 10×10 cm²

=> A = 100 cm²

Area of the square sheet of the paper

= 100 cm²

Given that

Length of the rectangular sheet

(l) = 25 cm

Let the breadth of the rectangular sheet be 'b' cm

We know that

Area of a rectangle is 'lb' sq.units

Area of the rectangular sheet

=> A = 25×b cm²

=> A = 25b cm²

Area of the rectangular sheet

= 25b cm²

According to the given problem

Area of the square sheet of the paper

= Area of the rectangular sheet

=> 100 = 25b

=> 25b = 100

=> b = 100/25

=> b = 4

Therefore, b = 4 cm

Now, we have,

Length (l) = 25 cm

Breadth (b) = 4 cm

We know that

Perimeter of a rectangle = 2(l+b) units

Perimeter of the rectangular sheet

=> P = 2(25+4) cm

=> P = 2(29) cm

=> P = 58 cm

Therefore, perimeter is 58 cm

Answer:-

The perimeter of the rectangular sheet is 58 cm

Used formulae:-

→ Area of a square of 's' units is 's²' sq.units

• s = side of the square

→ Area of a rectangle is 'lb' sq.units

→ Perimeter of a rectangle = 2(l+b) units

• l = length of the rectangle
• b = breadth of the rectangle

Answer 2

Answer:

Given :-

• The area of a square sheet of paper of side 10 cm is the same as that of a rectangular sheet of length 25 cm.

To Find :-

• What is the perimeter of the rectangle sheet.

Formula Used :-

♠ Area of Square Formula :

$\bigstar \: \: \sf\boxed{\bold{\pink{Area_{(Square)} =\: a^2}}}\: \: \: \bigstar$

where,

• a = Side of Square

♠ Area of Rectangle Formula :

$\footnotesize \bigstar \: \: \sf\boxed{\bold{\pink{Area_{(Rectangle)} =\: Length \times Breadth}}}\: \: \: \bigstar$

♠ Perimeter of Rectangle Formula :

$\footnotesize \bigstar \: \: \sf\boxed{\bold{\pink{Perimeter_{(Rectangle)} =\: 2(Length + Breadth)}}}\: \: \: \bigstar$

Solution :-

✯ First, we have to find the area of square sheet :

Given :

• Side = 10 cm

According to the question by using the formula we get,

$\implies \sf Area_{(Square\: Sheet)} =\: (10\: cm)^2$

$\implies \sf Area_{(Square\: Sheet)} =\: 10\: cm \times 10\: cm$

$\implies \sf\bold{\blue{Area_{(Square\: Sheet)} =\: 100\: cm^2}}$

✯ Now, we have to find the area of rectangular sheet :

Let,

$\mapsto \bf Breadth_{(Rectangular\: Sheet)} =\: x\: cm$

Given :

• Length = 25 cm

According to the question by using the formula we get,

$\implies \sf Area_{(Rectangular\: Sheet)} =\: 25\: cm \times x\: cm$

$\implies \sf\bold{\green{Area_{(Rectangular\: Sheet)} =\: 25x\: cm^2}}$

Now, given that :

✫ The area of a square sheet of paper is the same as that of a rectangular sheet.

So,

$\footnotesize \implies \bf Area_{(Square\: Sheet)} =\: Area_{(Rectangular\: Sheet)}$

$\implies \sf 100 =\: 25x$

$\implies \sf \dfrac{\cancel{100}}{\cancel{25}} =\: x$

$\implies \sf \dfrac{4}{1} =\: x$

$\implies \sf 4 =\: x$

$\implies \sf\bold{\purple{x =\: 4\: cm}}$

Hence, the breadth of a rectangular sheet is 4 cm .

✯ Finally we have to find the perimeter of a rectangular sheet :

Given :

• Length = 25 cm
• Breadth = 4 cm

According to the question by using the formula we get,

$\footnotesize \dashrightarrow \bf Perimeter_{(Rectangular\: Sheet)} =\: 2(Length + Breadth)$

$\dashrightarrow \sf Perimeter_{(Rectangular\: Sheet)} =\: 2(25 + 4)$

$\dashrightarrow \sf Perimeter_{(Rectangular\: Sheet)} =\: 2 \times 29$

$\dashrightarrow \sf\bold{\red{Perimeter_{(Rectangular\: Sheet)} =\: 58\: cm}}$

$\therefore$ The perimeter of a rectangular sheet is 58 cm .