Question

The perimeter of a rhombus is 60 cm. If one of its diagonals is 18 cm long, find

(i) the length of the other diagonal, and

(ii) the area of the rhombus.

Answer 1

Perimeter of a rhombus = 4a (Here, a is the side of the rhombus) 

⇒ `60=4a `

⇒ `a=15` 

(i) Given:

One of the diagonals is 18 cm long 

`d_1= 18cm` 

Thus, we have: 

Side= `1/2sqrt(d_1^2+d_2^2)` 

⇒ `15=1/2sqrt(18^2+d_2^2)` 

⇒`30=sqrt(18^2+d_2^2)` 

Squaring both sides, we get: 

⇒`900=18^2+d_2^2`

⇒`900=324+d_2^2` 

⇒`d_2^2=576` 

⇒`d_2^2=24cm`  

(ii) Area of the rhombus=`1/2d_1xxd_2` 

=`1/2xx18xx24` 

=`216 cm^2`