Question

if the diagonal of a rectangle is 3 times of its smallest side , then ratio of it sides is

Answer 1

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Answer 2

Answer:

$1:2\sqrt{2}$  

Step-by-step explanation:

Given : The diagonal of a rectangle is 3 times of its smallest side.

To Find: ratio of it sides

Solution :

Refer the attached figure.

AB is the largest side

BD is the diagonal

AD is the smallest side

Let the smallest side be x i.e. AD =x

Since we are given that diagonal of a rectangle is 3 times of its smallest side.

So, Diagonal = BD = 3x

Since we know that the angles of rectangle are of 90 °

Now in ΔABD

$Hypotenuse ^2=Perpendicular^2+Base^2$

$BD ^2=AD^2+AB^2$

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

$9x^2-x^2=AB^2$

$8x^2=AB^2$

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

$\sqrt{8}x=AB$

$2\sqrt{2}x=AB$

Now ratio of smallest side to the largest side=$\frac{x}{2\sqrt{2}x}$

                                                                          =$\frac{1}{2\sqrt{2}}$  

Hence the ratio of it sides is $1:2\sqrt{2}$