Question

if the length of the diagonal is three times one of its side , what will be the ratio of the sides of the rectangle ?​

Answer 1

Answer:

Let one = 1 cm

diagonal = 3 cm

so, other side by Pythagoras theoram we get :-----

other side = √3²-1² = 2√2

Required ratio of sides = 1:2√2 (Ans)

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Answer 2

Ratio of Length:Breadth=$\bold{ 2\sqrt2}:1}$

Step-by-step explanation:

Let us assume that,

Length of one side of rectangle = x = AB

Then,Length of the diagonal = 3x =AC

We know that,

In a rectangle ABCD,where AC is a diagonal

$(AC)^2= (AB)^2+(BC)^2$

$(3x)^2 = x^2+(BC)^2$

$(BC)^2=(3x)^2-(x)^2$

$(BC)^2=9x^2-x^2$

$(BC)^2 = 8x^2$

By taking Square root on both side,

$BC = \sqrt{8x^2}$

$BC=2\sqrt {2}x$

So,length of another side of the rectangle =$2\sqrt{2}x$

Now,Ratio of Length:Breadth =$2\sqrt{2}x:x$

Hence, Ratio of Length:Breadth=$\bold{ 2\sqrt2}:1}$