ABCD is a rectangle.the bisector of angle D divides diagonal AC in ratio 2:3.if one side of the rectangle is  3 cm,then the possible area of the rectangle is

Please help me my ftre is on sunday

Hi

 If diagonal AC is divided into ratio 2 : 3 then let be 2x and 3x

and can we the total length of diagonal will be 2x + 3x = 5x

If one side is 3x cm

If side AD is 3 cm

then what will be side CD

By pythagorastheorem we get side CD will be 4x cm

as 5x is hypotenuse and 3x is perpendicular.

Now the sides of triangle are 4x and 3x respectively.

Area of triangle = 1/ 2 * b * h

b = 4x

h = 3x

= 1/ 2 * 4x * 3x = 6x²

A rectangle is composed of two main triangles.

so area of reactange = l * b

= 4x * 3x =12x²

Therefore the possible area will be 12x² cm²

depending upon the value of x

Please give me thumbs up

Sorry by mistake i have taken the side to be two so the answer will be  nine cm square and four cm square