Question

find the length of the second diagonal of a rhombus, whose side is 10cm and one of the diagonal is 12cm.

Answer 1

a rhombus's diagonals bisect each other at their intersection point.
also they intersect at right angles.
halves of both the diagonals and a side form a right angled triangle.
half of the given diagonal is 12/2= 6 cm.
the side's length is 10 cm. (6,8,10) is a Pythagorean triplet, so the half of the other diagonal's length is 8 cm.
the other diagonal's length is 8x2= 16 cm.

Answer 2

Solution:-

let, Rhombus ABCD.

given:-

•The sides of a rhombus are 10cm and one diagonal is 12 cm .

let, DO = OB = ? , BD = ?

and AO = OC = 6cm, and AC = 12 cm

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 = (6)² + (OB)²

=> 100 = 36 + (OB)²

=> 100 - 36 = (OB)²

=> 64 = (OB)²

i.e.

=> (OB)² = 64

=> OB = √64

=> OB = 8 cm

so, we know

DO = OB = 8 cm

hence, BD = 16 cm

Area of rhombus = [(AC)×(BD)]/2

Area of rhombus = [ 12 × 16 ]/2

Area of rhombus = [192]/2

Area of rhombus= 96 cm²

Hence length of diagonal rhombus

is 16 cm and area of rhombus is

96 cm².

i hope it helps you.