Question

《QUESTION 1》
The length of the side of a square is 50 cm and the breadth of a rectangle is 25 cm. If the areas of the square and the rectangle are equal, find the length of the rectangle.

《QUESTION 2》
A wire is in the shape of a rectangle with length 6 cm. It is bent to form a square whose side is 5 cm. Find the breadth of the rectangle. Also, calculate the areas of both the rectangle and the square and find which shape encloses more areas.
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Answer 1

1) Length = 100 cm

2) Breadth = 4 cm

Ar(square) = 25 cm²

Ar(rectangle) = 24 cm²

Square encloses more area.

$\:$

Step-by-step explanation:

QUESTION 1 :-

The length of the side of a square is 50 cm and the breadth of a rectangle is 25 cm. If the areas of the square and rectangle are equal, find the length of the rectangle.

____________________

SOLUTION 1 :-

Remember,

• Area of square = (side)², i.e. side × side
• Area of rectangle = l × b
• where, l = length & b = breadth

Now, as given that,

• side of area = 50 cm
• Breadth of rectangle (b) = 25 cm

$\:$

A.T.Q.,

$\bf area \: of \: square = area \: of \: rectangle \\ \\ \bf = > side \times side = length \times breadth$

$\bf = > 50cm \times 50cm = l \times 25cm \\ \\ \bf = > \frac { \cancel{50} {}^{2} \times 50 {cm}^{2} }{ \cancel{25}cm} = l \\ \\ \bf = > l = 50 \times 2cm \\ \\ \bf = > \underline \blue{length = 100cm}$

Hence,

The length of the rectangle is 100 cm.

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QUESTION 2 :-

A wire is in the shape of a rectangle with length 6 cm. It is bent to form a square whose side is 5 cm. Find the breadth of rectangle. Also, calculate the areas of the rectangle and the square and find which shape encloses more area.

____________________

SOLUTION 2 :-

We have to remember,

• Perimeter of square = 4 × side
• Perimeter of rectangle = 2(l + b)
• Where, l = length & b = breadth

Given that,

• side of square = 5 cm
• Length of rectangle (l) = 6 cm

$\:$

A.T.Q,

Length of wire (in the shape of square) = Length of wire (in the shape of rectangle)

=> perimeter of square = perimeter of rectangle

$\\ \bf = > 4 \times side = 2(l + b) \\ \\ \bf = > 4 \times 5cm = 2 \times (6cm + b) \\ \\ \bf = > \frac{ \cancel {4}^{2} \times 5cm }{ \cancel{2}} = 6cm + b \\ \\ \bf = > 10cm = 6cm + b \\ \\ \bf = > 10cm - 6cm = b \\ \\ \bf = > 4cm = b \\ \\ \bf = > \underline \green{breadth = 4cm}$

Hence,

Breadth of the rectangle is 4 cm.

______________________

Now,

We have to find the areas of the shapes.

We know the formulas, we have the values. Let's begin.

$\:$

Area of square = side × side

$\bf = 5cm \times 5cm \\ \\ \bf = \underline \orange{25cm {}^{2} }$

Hence,

The area of square is 25 cm².

$\:$

Area of rectangle = length × breadth

$\bf = 6cm \times 4cm \\ \\ \bf = \underline \color{yellow}{24cm} {}^{2}$

Hence,

Area of rectangle is 24 cm².

$\:$

Since,

25 cm² > 24 cm²

=> Ar(Square) > Ar(Rectangle)

Hence,

Area of square encloses 1 cm² more than area of rectangle.

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Hope it helps.

#BeBrainly :-)

Answer 2

Step-by-step explanation:

ㅤㅤㅤQuestion (1)

Given information,

The length of the side of a square is 50 cm and the breadth of a rectangle is 25 cm. If the areas of the square and the rectangle are equal, we have to find the length of the rectangle.

Solution,

Formulae used here;

• Area of rectangle = Length × Breadth
• Area of square = (Side)²

According to the Question,

➻ Area of rectangle = Area of square

Putting all values we get,

➻ Length × Breadth = (Side)²

➻ Length × 25 = (50)²

➻ Length × 25 = 50 × 50

➻ Length × 25 = 2500

➻ Length = 2500/25

➻ Length = 100 cm

• Hence, length of rectangle is 100 cm.

ㅤㅤㅤQuestion (2)

Given information,

A wire is in the shape of a rectangle with length 6 cm. It is bent to form a square whose side is 5 cm. We have to find the breadth of the rectangle. Also, we have to calculate the areas of both the rectangle and the square and to that find which shape encloses more area.

Solution,

Formulae used here;

• Perimeter of rectangle = 2(Length + Breadth)
• Perimeter of square = 4 × side
• Area of rectangle = Length × Breadth
• Area of rectangle = Length × BreadthArea of square = (Side)²

As we know that same wire in shape of rectangle is bent to form square. Therefore;

➻ Perimeter of rectangle = Perimeter of square

Putting all values,

➻ 2(Length + Breadth) = 4 × side

➻ 2(6 + Breadth) = 4 × 5

➻ 12 + 2(Breadth) = 20

➻ 2(Breadth) = 20 - 12

➻ 2(Breadth) = 8

➻ Breadth = 8/2

➻ Breadth = 4 cm

• Hence, breadth of rectangle is 4 cm.

Now,

➻ Area of rectangle = Length × Breadth

Putting all values,

➻ Area of rectangle = 6 × 4

➻ Area of rectangle = 24 cm²ㅤ— (i)

• Hence, area of rectangle is 24 cm².

Now,

➻ Area of square = (Side)²

Putting all values,

➻ Area of square = (5)²

➻ Area of square = 5 × 5

➻ Area of square = 25 cm²ㅤㅤ— (ii)

• Hence, area of square is 25 cm².

From (i) and (ii) it is clear that;

ㅤ25 cm² > 24 cm²

ㅤArea of square > Area of rectangle

• Hence, square encloses more area as compared to rectangle.

Knowledge Booster,

• Perimeter of any figure is calculated by sum of it's all sides.
• Perimeter of square = 4 × side
• Area of square = (side)²
• Perimeter of equilateral ∆ = 3 × side
• Area of equilateral ∆ = √3/4 (side)²
• Perimeter of rhombus = 4 × side
• Area of rhombus = ½ × d₁ × d₂
• Perimeter of circle = 2πr
• Area of circle = πr²
• Perimeter of rectangle = 2(l + b)
• Area of rectangle = l × b

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