Question

ABCD is a rhombus .diagonals Ac=48cm and BD=14cm.find the perimeterof rombus ABCD.

Answer 1

Step-by-step explanation:

see the above photo

so perimeter=25*4=100 cm ans

Answer 2

Given:

ABCD is a rhombus.

Diagonal AC=48cm

Diagonal BD=14cm

To find:

The perimeter of rhombus ABCD

Solution:

We can find the perimeter by following the given steps-

We know that the diagonals of a rhombus are equal. These diagonals also bisect each other and divide them in half.

Let the point of intersection of both diagonal be E.

E divides AC and BD into two halves and is the mid-point.

AE=AC/2=48/2=24cm

EB=BD/2=14/2=7cm

The ∆AEB is a right-angled triangle as the diagonals bisect perpendicularly.

Using the Pythagoras theorem, we get

AE²+EB²=AB²

24²+7²=AB²

576+49= AB²

625=AB²

AB=25cm

All the sides of ABCD are equal since it's a rhombus.

AB=BC=CD=DA=25cm

The perimeter of the rhombus=Sum of all sides

=AB+BC+CD+DA

=25+25+25+25

=4×25

=100cm

Therefore, the perimeter of rhombus ABCD is 100 cm.