Question

the diagonal of a rectangle is thrice its smaller side . Find its ratio of its sides

Answer 1

see the pic..above..to know the answer.

Answer 2

Answer:

2√2 : 1

Step-by-step explanation:

Refer the attached figure

In rectangle ABCD

AB is the longer side

BC is the smaller side

AC is the diagonal

ΔABC is the right angled triangle since all angles of rectangle is of 90°.

Let the smaller side BC be x

Diagonal = AC = $3 \times \text{Smaller Side} = 3x$

So, In ΔABC

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

$AC^{2} = AB^2+ BC^2$

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

$9x^{2} = AB^2+ x^2$

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

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

$2\sqrt{2}x= AB$

Thus the longer side is $2\sqrt{2}x$

Smaller side = x

Ratio of its Sides = Longer side : smaller side

                            = 2√2x : x

                            = 2√2 : 1

Hence ratio of its sides is 2√2 : 1 .