Question

Adjacent sides of a rectangle are in the ratio of 5:12.If the perimeter of the rectangle is 34 cm. Find the length of the diagonal

Answer 1

given ratio between the adjacent sides of the rectangle 5 : 12

adjacent sides of a rectangle means it's breadth and length.

let the breadth and length of the rectangle be 5x and 12x respectively.

formula to find the perimeter of a rectangle = 2 ( l + b )

➡ 2 ( l + b ) = 34cm

➡ 2 ( 12x + 5x ) = 34cm

➡ 17x = 34/2

➡ 17x = 17

➡ x = 17/17

➡ x = 1

therefore it's breadth = 5x = 5cm

and it's length = 12x = 12cm

now by Pythagoras theorem we get,

➡ diagonal = √(length² + breadth²)

➡ diagonal = √(12² + 5²)

➡ diagonal = √(144 + 25)

➡ diagonal = √169

➡ diagonal = 13cm

hence, the Length of the diagonal is 13cm.

Answer 2

Answer:

Diagonal = 13 cm

Step-by-step explanation:

Ratios = 5:12

Let the breadth be 5x

and lenth be 12x

So,

_____________________________

We have formula:

2(l+b) = Perimeter

_____________________________

Perimeter = 2(l+b)

__________________[Put values]

34 = 2(5x + 12x)

34 = 2(17x)

34 = 34 x

x = 34/34

x = 1

Length = 12 x

» 12(1)

» 12 cm

Breadth = 5x

» 5(1)

» 5 cm

_____________________________

Pythagoras theorem

H² = P² + B²

______________________________

Diagnol² = Length² + breadth²

Diagnol² = (12)² + (5)²

Diagonal² = 144 + 25

Diaginal² = 169

diagonal = √169

Diagonal = 13

_____________________[Answer]

So, Diagonal of rectangle is 13 cm