Question

Adjecent side of a rectangle
ratio of 5:12. If the perinator of the rectangle
is 34m, find the length of the diagonal​

Answer 1

{some correction in question}

Question : Adjecent side of a rectangle are in ratio of 5:12. If the perimeter of the rectangle is 34 m, find the length of its diagonal ?

Solution : Let, first side of rectangle be 5x and second side of rectangle be 12x.

⟹ breadth = second side = 5x ____( 1 )

⟹ length = first side = 12x _____( 2 )

{Properties of rectangle :

• The opposite sides are parallel and equal to each other.
• Each interior angle is equal to 90 degrees.}

Now, by formula of perimeter of rectangle :

⟹ perimeter of rectangle = 2 * (length + breadth)

⟹ 34 = 2 * (12x + 5x)

⟹ 34 = 2 * 17x

⟹ 34 = 34x

⟹ x = 34/34

⟹ x = 1

Now put value of x in equation ( 1 ) and equation ( 2 )

⟹ breadth = second side = 5x

⟹ breadth = second side = 5 * 1

⟹ breadth = second side = 5 m

and

⟹ length = first side = 12x

⟹ length = first side = 12 * 1

⟹ length = first side = 12 m

Let, diagonal of rectangle be hypotenuse

Now, by Pythagoras theorem :

⟹ (hypotenuse)² = (first side)² + (second side)²

⟹ (hypotenuse)² = ( 12 )² + ( 5 )²

⟹ (hypotenuse)² = 144 + 25

⟹ (hypotenuse)² = 169

⟹ hypotenuse = √169

⟹ hypotenuse = 13 m

Answer : Hence, diagonal of the rectangle is 13 m.

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