Question

The perimeter of a rectangle is equal to 280 meters. The ratio of its length to its width is 5:2. Find the area of the rectangle in sq.m *

Answer 1

Answer:

Step-by-step explanation:

Given :-

Perimeter of rectangle = 280 m

Ratio of its length to width = 5 : 2

To Find :-

Area of rectangle

Formula to be used :-

Perimeter of rectangle = 2(l + b)

Area of rectangle = Length × Breadth

Solution :-

Putting all the values, we get

Let the length and width be 5x and 2x.

Perimeter of rectangle = 2(l + b)

Perimeter of rectangle = 280 m

⇒ 2(l + b) = 280 m

⇒ 2(5x + 2x) = 280 m

⇒ 2 × 7x = 280 m

⇒ 14x = 280

⇒ x = 280/14

⇒ x = 20

Length = 5x = 5 × 20 = 100 m

Width = 2x = 2 × 20 = 40 m

Now, area of the rectangle,

Area of rectangle = l × b

⇒ Area of rectangle = 100 × 40

⇒ Area of rectangle = 4000 m²

Hence, the Area of rectangle is  4000 m²,

Answer 2

$\huge\sf\red{Answer:}$

☆ Given:

⇒ The perimeter of a rectangle is equal to 280 meters. The ratio of its length to its width is 5:2.

☆ Find:

⇒ Find the area of the rectangle in m².

☆ According to the question:

⇒ Let us assume '5x' and '2x' as length and width.

☆ Using formula:

$\sf\green{Perimeter \: of \: Rectangle = 2 \: (Length + Breadth)}$

☆ Calculations:

⇒ $\sf 2 \: (Length + Breadth) = 280 \: m$

⇒ $\sf 2 \: (5x + 2x) = 280$

⇒ $\sf (2 × 7x) = 280$

⇒ $\sf 14x = 280$

⇒ $\sf \dfrac{280}{14}$

⇒ ${\sf{\underline{\boxed{\green{\sf{20}}}}}}$

☆ Adding values from the above equation, we get:

⇒ $\sf Length = 5x = (5 \times 20) = 100 \: m$

⇒ $\sf Width = 2x = (2 \times 20) = 40 \:m$

⇒ $\sf\green{Using \: formula: [Length \times breadth]}$

☆ Finding the area of rectangular:

⇒ $\sf 100 \times 40 = 4000$

⇒ ${\sf{\underline{\boxed{\green{\sf{ 4000 \: m^2}}}}}}$

Therefore, 4000m² is the area of rectangle.