Question

If length of a diagonal of a rhombus is 30 cm and it's area is 240 sq cm, find the perimeter

Answer 1

The perimeter is 68 cm.

Step-by-step explanation:

Given information: Diagonal of a rhombus = 30 cm and Area = 240 sq cm.

Area of a rhombus:

$Area=\dfrac{1}{2}(d_1\times d_2)$

where, d1 and d2 are diagonal of the rhombus.

$240=\dfrac{30\times d_2}{2}$

$240=15d_2$

Divide both sides by 15.

$16=d_2$

The length of second diagonal of the rhombus is 16 cm.

Diagonals of a rhombus are pericardium bisector.

Let length of each side of the rhombus be x.

$x=\sqrt{(\dfrac{d_1}{2})^2+(\dfrac{d_2}{2})^2}$

$x=\sqrt{(\dfrac{30}{2})^2+(\dfrac{16}{2})^2}$

$x=\sqrt{(15)^2+(8)^2}$

$x=\sqrt{289}$

$x=17$

Perimeter of the rhombus is

$4x=4(17)=68$

Therefore, the perimeter is 68 cm.

#Learn more

The area of a rhombus is 240 cm sq. and one of the diagonal is 16 cm. Find the other diagonal.

https://brainly.in/question/2766481