Question

the perimeter of a rhombus is 164 M if length of 1 of diagonal is 18 M find the length of other diagonal hence the find the area of Rhombus

Answer 1

This is ur answer hope it will help u in case of any doubt comment below

Answer 2

Length of other diagonal is 80 cm and area of Rhombus is 720 cm2.

Step-by-step explanation:

Given:

Let the diagonals AC and BD of a rhombus ABCD meet at O. Diagonal AC= 18 cm , diagonal BD=?

Length of each side = $\frac{Perimeter of rhombus}{4} = \frac{164}{4} = 41 cm$

or AB=BC=CD=AD= 41 cm.

In right angled triangle AOB,

$AO^2+OB^2=AB^2$

$(\frac{AC}{2} )^2+(\frac{BD}{2} )^2= 41^2$    $[AO=\frac{AC}{2}, OB=\frac{BD}{2} ]$

$(\frac{18}{2} )^2+(\frac{BD}{2} )^2= 41^2$

$(9 )^2+(\frac{BD}{2} )^2= 41^2$

$(\frac{BD}{2} )^2= 1681-81$

$(\frac{BD}{2} )^2= 1600$

$\frac{BD}{2}=\sqrt{1600}$

$\frac{BD}{2}=40$

BD = 80 cm.

Area of rhombus = $\frac{1}{2}\times diagonal_1 \times diagonal_2$

                            = $\frac{1}{2}\times AC \times BD$

                             = $\frac{1}{2}\times 18 \times 80$

                             = $9 \times 80$

                             = $720 cm^2$

Hence length of other diagonal is 80 cm and area of Rhombus is $720 cm^2$.