Question

In a rhombus, if diagonals are 30cm and 40cm, find its perimeter .

Answer 1

Answer is in the above pic.

Answer 2

$<b>Heya mate. (^_-). Solution below.$
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[] Refer to the attachment for the figure.



[] Let ABCD be the rhombus, in which,

AC = 30 cm

BD = 40 cm


• Now, we know that diagonals of a rhombus bisect each other at right angles.


Then,

AO = ½ AC = 1/2 × 30 = 15 cm

BO = ½ BD = 1/2 × 40 = 20 cm

angle AOB = 90°

=>>That makes a right angled triangle angled at O.

=>> So, side opposite to angle O, i.e. AB is the hypotenuse.


• Then, by Pythagoras' Theorem,

AB² = AO² + BO²

= 15² + 20²

= 225 + 400

= 625

=>> AB² = 625

=> AB = √625

=> AB = 25

•°• One side of the rhombus is 25 cm



[] Now, we know that, all sides are equal in a rhombus.

=> AB = BC = CD = DA = 25cm



[] Now, the perimeter,

= sum of all sides

= AB + BC + CD + DA

= 25 + 25 + 25 + 25

= 100 cm.

•°• The Perimeter of the rhombus = 100 cm


$<marquee>Hence, the perimeter is 100 cm.</marquee>$
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Thank you... ;-)