Question

if length of a diagonal of a rhombus is 30 cm and its area is 240 sq cm find its perimeter ​

Answer 1

If the length of a diagonal of a rhombus=30cm

Area =240cm^2

Let's take the length of the other diagonal be x

The formula for finding the area of rhombus is 1/2*first diagonal *second diagonal

According to question : The product of 1/2,first diagonal =30 and second diagonal =x gives the result area of the rhombus =240cm^2

So, 1/2*30*x=240

=>1*15*x=240

=>15x=240

=>x=240/15

=>x=16

Since, the second diagonal is 16cm

The half of first diagonal =30/2=15

The half of second diagonal =16/2=8

Since, all sides of the rhombus are equal

So we should use the pythagorean theorom, that is side=root over of(15) ^2 +(8)^2 =root over of 225+64=root over of289=17

Since, all sides of the rhombus are equal

Perimeter =17*4=68cm

Therefore the perimeter is 68cm

HOPE THIS WILL HELP YOU