Question

The area of a rhombus is 480 cm², and one of its diagonals measures 48 cm. Find

(i) the length of the other diagonal,

(ii) the length of each of its sides, and

(iii) its perimeter.

Answer 1

(i) Area of a rhombus, =` 1/2xxd_1xxd_2`, Where `d_1  and  d_2` are the lengths of the diagonals. 

⇒ `480=1/2xx48xxd_2` 

⇒`d_2=(480xx2)/48` 

⇒ `d_2=20 cm` 

∴ Length of the other diagonal=`20cm` 

(2) side=`1/2 sqrt(d_1^2-d_2^2)` 

= `1/2sqrt(48^2+20^2)` 

=`1/2sqrt(2304+400)` 

=`1/2sqrt2704` 

=`1/2xx52` 

=`26 cm` 

∴ Length of the side of the rhombus =`26cm` 

(iii) Perimeter of the rhombus=`4xx"side"` 

=`4xx26` 

=`104 cm`