Question

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***the perimeter of a rectangular sheet is 170 cm if the its breadth is 20 cm more than its length find the length and find the area also***​

Answer 1

Answer:

The area of the rectangular sheet is 1706.25 cm².

Step-by-step explanation:

Given :

Perimeter of the Rectangle = 170 cm

Its breadth = 20 cm more than its length

To find :

Its length and area

Solution :

Consider the -

• Length as x
• Breadth as (x + 20)

$\bigstar{\boxed{\sf{Perimeter=2(Length+Breadth)}}}$

$\sf{\longrightarrow} \: 2(x + x + 20) = 170 \\ \\ \sf{\longrightarrow} \: 2x + 2x + 40 = 170 \\ \\ \sf{\longrightarrow} \: 4x + 40 = 170 \\ \\ \sf{\longrightarrow} \: 4x = 170 - 40 \\ \\ \sf{\longrightarrow} \: 4x = 130 \\ \\ \sf{\longrightarrow} \: x = \frac{130}{4} \\ \\ \sf{\longrightarrow} \: x = 32.5$

Length = 32.5 cm

$\rule{300}{1.5}$

★ Value of (x + 20)

$\sf{\longrightarrow} \: 32.5 + 20 \\ \sf{\longrightarrow} \: 52.5$

Breadth = 52.5 cm

• Length is 32.5 cm
• Breadth is 52.5 cm

$\rule{300}{1.5}$

★ $\boxed{\sf{Area=Length \times Breadth}}$

$\sf{\longrightarrow} \: 32.5 \times 52.5 \\ \sf{\longrightarrow} \: 1706.25 \: {cm}^{2}$

$\therefore$ The area of the rectangular sheet is 1706.25 cm².

Answer 2

Answer:

Step-by-step explanation:

Given :-

Perimeter of the Rectangle = 170 cm

Its breadth is 20 cm more than its length .

To Find :-

Length and Area of rectangular sheet.

Formula to be used :-

Perimeter of rectangle = 2 × (Length + Breadth)

Area of rectangle = Length × Breadth

Solution :-

Let the Length be x and Breadth be x + 20.

According to the Question

Perimeter of rectangle = 2 × (Length + Breadth)

⇒ 2 × (x + x + 20) = 170

⇒ 2 × (2x + 20) = 170

⇒ 4x + 40 = 170

⇒ 4x = 170 - 40

⇒ 4x = 130

⇒ x = 130/4

⇒ x = 32.5

Length of rectangular sheet = x = 32.5 cm

Breadth of rectangular sheet = x + 20 = 32.5 + 20 = 52.5 cm

Area of rectangular sheet = Length × Breadth

Area of rectangular sheet = (32.5 × 52.5) cm²

Area of rectangular sheet = 1706.25 cm²

Hence, Length and breadth of rectangular sheet is 32.5 cm and 52.5 cm.

And Area of rectangular sheet is 1706.25 cm².