Question

if diagonals of a rhombus are 18cm and 24cm then its perimeter is

Answer 1

The diagonal of a rhombus bisect each other at 90 degrees... So they will form four right angled triangle....
Applying Pythagoras theorem...
Side²=9²+12²
Side²=81+144
Side²=225
Side=15 cm

Perimeter.=4* side
4*15=60 cm

Answer 2

Heya mate, Here is ur answer

We know that the diagonals of Rhombus bisect each other at 90° .

And 90° means right angled ∆ . So, to find a side of the rhombus (that will be hypotenuse of the ∆ , we will be using PGT -Pythagoras Theorem)

What is Pythagoras Theorem ❓❓

According to Pythagoras theorem, the sum of the squares of other two sides in a right angled ∆ , gives the square of the hypotenuse.

So, now let's move on to the question.

Given : Diagonal$\tiny{1}$=18 cm.

Diagonal $\tiny{2}$=24 cm.

In rhombus,diagonals bisect each other at 90° , So the dimensions of the right angled Triangle becomes :

$\frac{diagonal \: 1}{2}$

$= \frac{18}{2}$

=9 cm

$\frac{diagonal \: 2}{2}$

$= \frac{24}{2}$

=12 cm

Hypotenuse = Side of rhombus =? .

Using PGT in the Triangle.

${hypo}^{2} = {base}^{2} + {pependicular}^{2}$


$side {}^{2} = 9 {}^{2} + 12 {}^{2}$


$side {}^{2} = 81 + 144$

$side {}^{2} = 225$

$side = \sqrt{225}$

side =15 cm.

Perimeter of Rhombus=4×side

=4×15

=60 cm.

Warm regards

@LaughterQueen

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