Question

the area of a rhombus is 480cm2and one of its diagonal measures 48cm .find the length of other diagonal ,the length of each sides and its perimeter

Answer 1

let d1 and d2 be the diagonals of rhomus and length of its each sides be 'a'.

Given , area of rhombus = 480 cm^2

diagonal 1 ( d1 ) = 48 cm

since, we know that

Area of rhomus = d1 × d2 / 2

d1 × d2 / 2 = 480 cm^2

48 × d2 = 480 × 2

d2 = 20 cm

since, we know that

diagonal of rhomus bisects at 90° and length of each sides of rhomus are always equal.

so then ,OB = BD / 2 = 20/ 2 = 10 cm

OB = OD = 10 cm

and AO = AC / 2 = 48 / 2 = 24 cm

AO = OC = 24 cm

from ∆ AOB :
-------------------
by Pythagoras theorm , we get

( AB )^2 = ( OB )^2 + ( AO )^2

a^2 = ( 10 )^2 + ( 24 )^2

a^2 = 100 + 576

a^2 = 676 => a = √676

a = 26 cm

a = side = 26 cm

perimeter of rhombus = 4 × side

= 4 × 26 = 104 cm

therefore ,

length of other diagonal = 20 cm

length of each sides of rhombus =26cm

perimeter of rhombus = 104cm

Answer:d2 =20cm,a=26 cm,p = 104 cm

--------------------------------------------------------

Answer 2

The length of other diagonal is 20 cm. Length of each side is 26 cm. Perimeter of rhombus is 104 cm.