Question

the perimeter of a rhombus is 52 cm and one of its diagonals is 24 cm find the other diagonal and the area of the rhombus

Answer 1

First we need to find side.

Side of rhombus = Perimeter ÷ 4

=> side = 52/4

=> side = 13


We can apply Pythagoras Theorem to find out the length of diagonal.

Refer the attachment to see how.

We know that diagonal of a rhombus bisect each other at right angle.

So, the right angled triangle formed by diagonals has its hypotenuse as the side and the perpendicular and bases are half of diagonal.

We are given one diagonal = 24cm
Half = 12cm

Now by Pythagoras theorem,

12² + (d/2)² = 13²

=> (d/2)² = 13² - 12²

=> (d/2)² = 169 - 144

=> (d/2)² = 25

=> d/2 = √25

=> d/2 = 5

=> d = 5 × 2

=> d = 10cm


Other diagonal = 10cm


Area of rhombus = 1/2 × diagonal one × diagonal two

=> area = 1/2 × 24 × 10

=> area = 120cm²


Hope it helps dear friend ☺️✌️

Answer 2

$\bold{\huge{\underline{\mathcal{\star\:Hey \: mate\:\star}}}}$

$<b><i>Here's ur answer <i><b>$

✨ Diagonals of a rhombus bisect each other at 90 degrees 

✨ Half of each diagonal and one side would for a right angled triangle with the side of the rhombus as the hypotenuse 

One side is 52cm/4 = 13cm 
Half of given diagonal is 12cm

Half of the other diagonal is
√(13² - 12²) = 5cm

The other diagonal is 5×2=10cm

Area of rhombus = half product of diagonals = (1/2) × 10cm × 24cm =

Answer= 120cm²

$<u>Hope it helps you </u>$