Question

if the length and breadth of a rectangle are in the ratio 4:5 and its area =8000cm² find its perimeter​

Answer 1

Explanation:

Given

• The ratio between the length and breadth of a rectangle is 4:5
• The area of the rectangle is 8000cm²

To Find

• The perimeter of the rectangle.

Solution

Let the greatest common factor between the length and breadth of the rectangle is "a"

Then,

The length of the rectangle = 4a

The breadth of the rectangle = 5a

The area of a rectangle is the product of its length and breadth.

Area of a rectangle = Length × Breath

⟹ 8000cm² = 4a × 5a

⟹ 8000cm² = ( 4 × 5 )a²

⟹ 8000cm² = 20a²

⟹ 8000cm²/20 = a²

⟹ 400cm² = a²

⟹ √(400cm²) = a

⟹ 20cm = a

We've got the value of common factor between the length and breadth i.e. 20cm.

The length of the rectangle

⟹ 4a

⟹ 4( 20cm )

⟹ 80 cm

The breadth of the rectangle

⟹ 5a

⟹ 5( 20cm )

⟹ 100 cm

As now we've both the length and breadth of the rectangle, we can find the perimeter:

Perimeter of a rectangle = 2( length + breadth )

Perimeter of the rectangle = 2( 80cm + 100cm )

Perimeter of the rectangle = 2( 180cm )

Perimeter of the rectangle = 360cm

360 cm is the perimeter of the rectangle.