Question

each side of a rhombus is 10cm long and one of its diagonals measures 16cm .find the length of the other diagonal and hence find the area of the rhombus.........(step by step)....

Answer 1

let the side be a and diagonal s are d1&d2
then remember a2=1/2d1 *1/2d2
therefore 100=1/2*16 *1/2d2
100=8*1/2*d2
100=4*d2
d2=25 cm hence the length of another diagonal is 25 cm

Answer 2

Solution:-

let, Rhombus ABCD.

given:-

•The sides of a rhombus are 10cm and one diagonal is 16cm .

let, DO = OB = 8 cm, BD = 16 cm

and AO = OC = ?

1) we know diagonal of rhombus are equally bisect each other and they are perpendicular to each other.

2) All sides of rhombus are equal.

so,

by Pythagoras theorem.

=> (AB)² = ( AO )² + ( OB )²

=> (10)² = (AO)² + (8)²

=> 100 = (AO)² + 64

=> 100 - 64 = (AO)²

=> 36 = (AO)²

i.e.

=> (AO)² = 36

=> AO = √36

=> AO = 6 cm

so, we know AO = OC = 6 cm

hence, AC = 12 cm

Area of rhombus = [(AC)×(BD)]/2

Area of rhombus = [ 12 × 16]/2

Area of rhombus = [192]/2

Area of rhombus= 99.84 cm²

Hence length of diagonal rhombus

is 12 cm and area of rhombus is

96 cm².

i hope it helps you.