Question

A pair of adjacent sides of rectangle are in the ratio 3:4.If it's diagonal is 20cm long,f Ind the length of the sides and perimeter of the rectangle.

Answer 1

Let us consider the triangle formed by the diagonal of length 20 cm.

Using the ratio 3:4 =b:l

let the common multiplier be 'x'
Therefore,

Length = 4x

Breadth = 3x

Using Pythagoras theorem

${diagonal}^{2} = {3x}^{2} + {4x}^{2}$

$400 = 9 {x}^{2} + 16 {x}^{2}$
$400 = 25 {x}^{2}$
$\frac{400}{25 } = {x}^{2}$
The common multiplier is 4.

Therefore the dimensions of the rectangle is

3x = 3 × 4 = 12 cm ...... Breadth

4x = 4 × 4 = 16 cm ...... Length

Perimeter is 2(l + b)

2(28)

56 cm