Question

If length of a diagonal of a rhombus is 30 cm and its area is 240 sq cm, find its perimeter.

Answer 1

Length of Diagonal 2= 16cm
Side of rhombus= 17cm
Perimeter of rhombus=68cm

Hope it helps...!!!

Answer 2

Answer:

Perimeter=68

Step-by-step explanation:

Given: Length of the diagonal of a rhombus is 30 cm and area is 240 sq cm.

Since diagonals of the rhombus bisects each other at 90°,therefore OA=OC=15cm.

Now, Area of rhombus=$\frac{d_{1}{\times}d_{2}}{2}$, where $d_{1}$ and $d_{2}$ are the two diagonals of rhombus.

⇒$240=\frac{d_{1}{\times}d_{2}}{2}$

⇒$240{\times}2=30{\times}d_{2}$

⇒$d_{2}=16$

Now, OB=OD=8

From ΔAOB, using Pythagoras theorem,

$(AB)^{2}=(AO)^{2}+(OB)^{2}$

⇒$(AB)^{2}=(15)^{2}+(8)^{2}$

⇒$(AB)^{2}=225+64$

⇒$AB=17$

Since, in rhombus all four sides areequal, therefore, AB=BC=CD=DA=17

Now, perimeter of rhombus is= $4{\times}side$

                                                 =$4{\times}17$

                                                 =$68$