Question

a pair of adjecent sides of a rectangle are in the ratio3:4 and it's diognal is 20cm find the lenth of the sides and hence the perimeter of the rectanlei​

Answer 1

Answer:

The ratio of the adjacent sides of a rectangle = 3 : 4

The adjacent sides of a rectangle are its length and breadth.

(adjacent sides = Any two sides with a common end-point are called the adjacent sides of the rectangle)

∴ => length : breadth = 3 : 4

Let the sides of the rectangle be 3x and 4x (x is a common factor of length and breadth of the rectangle)

Given, length of diagonal = 20cm

Length of diagonal = √(l² + b²)

[Where,

• l = length of the rectangle
• b = breadth of the rectangle]

=> 20 cm = √(l² + b²)

(squaring both the sides) :-

=> (20)² = l² + b²

=> (20)² = (3x)² + (4x)²

=> 400 = 9x² + 16x²

=> 400 = 25x²

=> 16 = x²

=> √(16) = x

=>x=4

Hence, the common factor of length and breadth of the rectangle is 4.

• Length = 3 x 4 = 12cm

• Breadth = 4 x 4 = 16cm

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PERIMETER of a rectangle = 2 x (l + b)

= 2 x (12 + 16)

= 2 x 28

= 56 cm

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Answer :-

1. Length = 12cm
2. Breadth = 16cm
3. The perimeter of the rectangle is 56 cm.