Question

The diagonal of a rhombus is 16cm and side is 10cm. Find its other diagonal and area?? ​

Answer 1

Answer:

Diagonals of rhombus intersect each other at right angles and bisect each other. So half of each diagonals can be considered as perpendicular and base and side of rhombus can be treated as hypotenuese. ans=12cm , 96cm²

Step-by-step explanation:

half of diagonal=8cm(16/2)

hyp=10cm(side of rhombus)

So c²=a²+b²

10²=8²+b²

b=6

diagonal =2*b=12

Area = product of diagonals*.5(formula)

=16*12/2=96cm sq

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.