Question

the diogonals of rhombus are in ratio 3:4.if it's peri. is 40 .find the lengths of the sides and diogonals of the rhombus.​

Answer 1

Step-by-step explanation:

Perimeter =40cm

Side= 40/4

=10 cm

As diagonal cut each other at right angle,

3x/2^2+2x^2=10^2

9x^2/4+4x^2=100

9x^2+16x^2=400

25x^2=400

x^2=400/25

x= root 400/25

x= 4 cm

Length of diagonal=3x= 3*4=12cm,4x=4*4=16cm

Answer 2

Answer:

12units and 16units

Step-by-step explanation:

let diagonals be 3x and 4x

perimeter of rhombus=4s=40

                                    =s=40/4=10

s=10units

Now we know diagonals of rhombus are perpendicular bisectors of each other.

∴new length of diagonals are 2x and 1.5x

Apply pythagoras rule with side being hypotenuse

10²=(2x)²+(1.5x)²

100=4x²+  2.25x²

100=6.25x²

100/6.25=x²

16=x²

√16=x

4=x

x=4

put value of x=4 in 4x and 3x

we get 16units and 12 units.

∴diagonals are 16 units and 12 units.