Question

08] A rectangle and a square are of equal area. If the length and
the perimeter of a rectangle are 25 cm and 58cm, respectively,
then find the perimeter and area of the square​

Answer 1

Answer:

• Perimeter of square is 40 cm.
• Area of square is 100 cm².

Step-by-step explanation:

Given :-

• Area of rectangle and area of square are equal.
• Length of rectangle is 25 cm.
• Perimeter of rectangle is 58 cm.

To find :-

• Perimeter of square.
• Area of square.

Solution :-

• First we will find area of rectangle. We do not have breadth of rectangle. So, by using perimeter and length of rectangle we will find breadth of rectangle.

Let, Breadth of rectangle be x cm.

Perimeter of rectangle = 2(Length + Breadth)

$\longrightarrow$ 58 = 2(Length + Breadth)

$\longrightarrow$ 58 = 2×(25 + x)

$\longrightarrow$ 58 = 50 + 2x

$\longrightarrow$ 58 - 50 = 2x

$\longrightarrow$ 8 = 2x

$\longrightarrow$ x = 8/2

$\longrightarrow$ x = 4

We take breadth be x. So, Breadth of rectangle is 4 cm.

Now,

Area of rectangle = Length × Breadth

$\longrightarrow$ Area = 25 × 4

$\longrightarrow$ Area = 100

Area of rectangle is 100 cm².

• It is given that areas of square and rectangle are equal.

Thus, Area of square is 100 cm².

• We need side of square for perimeter. So by using area we will find side of square.

Area of square = Side × Side [Or, (Side)² ]

$\longrightarrow$ 100 = (Side)²

$\longrightarrow$ Side = √100

$\longrightarrow$ Side = 10

Side of square is 10 cm.

We know,

Perimeter of square = 4 × side

$\longrightarrow$ Perimeter = 4 × 10

$\longrightarrow$ Perimeter = 40

Therefore,

Perimeter of square is 40 cm.

Answer 2

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Let it be x

Perimeter of rectangle = 2(Length + Breadth)

• 58 = 2(Length + Breadth)
• 58 = 2×(25 + x)
• 58 = 50 + 2x
• 58 - 50 = 2x
• 8 = 2x
• x = 8/2
• x = 4

We take breadth be x. So, Breadth of rectangle is 4 cm.

Now,

Area of rectangle = Length × Breadth

→ Area = 25 × 4

→ Area = 100

Area of rectangle is 100 cm².

Thus, Area of square is 100 cm².

Area of square = Side × Side

→ 100 = (Side)²

→ Side = √100

→ Side = 10

Side of square is 10 cm.

We know,

Perimeter of square = 4 × side

→ Perimeter = 4 × 10

→ Perimeter = 40

Therefore,

Perimeter of square is 40 cm.