Question

is the perimeter of a rectangular field whose diagonal is 29 m and breadth is 20m​

Answer 1

Answer:

The perimeter of the rectangle is 82 m.

Step-by-step-explanation:

We have given that,

Diagonal of rectangle = 29 m

Breadth of rectangle = 20 m

We have to find the perimeter of the rectangle.

Now, we know that,

In a rectangle, length and breadth are perpendicular to each other and the diagonal is hypotenuse of the right triangle formed.

Now, by Pythagoras theorem,

( Diagonal )² = ( Length )² + ( Breadth )²

⇒ ( 29 )² = L² + ( 20 )²

⇒ L² = ( 29 )² - ( 20 )²

⇒ L² = ( 29 + 20 ) ( 29 - 20 ) - - - [ ∵ a² - b² = ( a + b ) ( a - b ) ]

⇒ L² = 49 * 9

⇒ L = √( 49 * 9 )

⇒ L = √( 7 * 7 * 3 * 3 )

⇒ L = 7 * 3

⇒ L = 21

∴ Length = 21 m

Now, we know that,

Perimeter of rectangle = 2 ( Length + Breadth )

⇒ Perimeter of rectangle = 2 ( 21 + 20 )

⇒ Perimeter of rectangle = 2 * 41

⇒ Perimeter of rectangle = 82 m

∴ The perimeter of the rectangle is 82 m.