Question

the digonal of a rectangle is thrice its smaller side. find the ratio of its sides [hint use phythagoras theorem]

Answer 1

Answer:

The ratio of its sides is 2√2 : 1

Step-by-step explanation:

We know that all sides of rectangle are perpendicular( at 90° )  to each other.

Therefore,

length^2 + breadth^2 = diagonal^2

According to the question, diagonal of the rectangle is thrice its smaller side( breadth ). Let the breadth x , so diagonal should 3 times of x i.e. 3x

Now,

= > length^2 + x^2 = ( 3x )^2

= > length^2 + x^2 = 9x^2

= > length^2 = 9x^2 - x^2

= > length^2 = 8x^2

= > length = √8x^2

= > length = 2x√2

Therefore,

Ratio of length to breadth = 2x√2 : x

                                   = 2√2 : 1

Therefore the ratio of its sides is 2√2 : 1

Answer 2

All sides of rectangle are perpendicular to each other.

So measure = 90°

Hence :-

L² + B² = D²

=>Length² + Breadth² = Diagonal²

Assume the breadth P , so diagonal should 3 times of P = 3p

Now,

= > length² + p² = ( 3p )²

= > length² + p² = 9p²

= > length² = 9p² - p²

= > length² = 8p²

= > length = √8p²

= > length = 2p√2

Since,

Ratio of length and to the breadth will be = 2p√2 : p

                                   = 2√2 : 1