Question

the area of a rhombus is 480cmsquare, and one of its diagonals measures 48cm. find(1) the length of the other diagonals,(2) the length of each of its sides, and (3) it's perimeter.

Answer 1

Let ABCD is a rhombus , in which AB and CD are it's two diagonals.



Let AB = 48 cm and CD = x cm.


Area of rhombus ABCD = 480



1/2 × AB × CD = 480


1/2 × 48 × x = 480




X = ( 480 × 2 / 48 ) cm


X = 20 cm.


Length of diagonal CD = x = 20 cm.






As , we know that the diagonals of a rhombus bisect each other at right angled.



OA = OB = 1/2 × AB = 24 cm.


And,

OC = OD = 1/2 × CD = 10 cm.



In right angled triangle OAC ,



OA = 24 cm and OC = 10 cm.



By Pythagoras theroem,


AC² = (OA)² + (OC)²



AC² = (24)² + (10)²



AC² = 676



AC = √676


AC = 26 cm.


Side AC = AD = BD = BC = 26 cm.







Perimeter of rhombus = 4 × Side = 4 × 26 = 104 cm.

Answer 2

Answer:

Step-by-step explanation:

Let ABCD is a rhombus , in which AB and CD are it's two diagonals.

Let AB = 48 cm and CD = x cm.

Area of rhombus ABCD = 480

1/2 × AB × CD = 480

1/2 × 48 × x = 480

X = ( 480 × 2 / 48 ) cm

X = 20 cm.

Length of diagonal CD = x = 20 cm.

As , we know that the diagonals of a rhombus bisect each other at right angled.

OA = OB = 1/2 × AB = 24 cm.

And,

OC = OD = 1/2 × CD = 10 cm.

In right angled triangle OAC ,

OA = 24 cm and OC = 10 cm.

By Pythagoras theroem,

AC² = (OA)² + (OC)²

AC² = (24)² + (10)²

AC² = 676

AC = √676

AC = 26 cm.

Side AC = AD = BD = BC = 26 cm.

Perimeter of rhombus = 4 × Side = 4 × 26 = 104 cm.