Question

the perimeter of a rhombus is 100cm and one of the diagonal is 40cm then the area of the rhombus in square cm

Answer 1

Perimeter = 100 cm

In Rhombus all sides are equal so for getting lenght of one side we need to divide perimeter by 4 sides.

= 100 / 4
= 25 cm is lenght of each side.

Area of Rhombus = lenght of each diagonal / 2.
Inside the rhombus there forms a triangle with hypotenuse 25cm.

And one of side as 20cm. Which is half lenght of one diagonal.

So by Pythagoras method half lenght of other diagonal is

15cm.

So other diagonal would be 2 × 15 = 30cm.

Area = 30 × 40 / 2 = 600 sq. cm.

Hope it helps!

Answer 2

The correct answer is 600 $cm^{2}$.

Given: Perimeter of rhombus = 100 cm.

Length of one diagonal = 40 cm.

To Find: Area of rhombus.

Solution:

As all the sides of rhombus are equal.

Let side  = x

Perimeter = 4x

4x = 100

x = 25

Side = 25 cm.

Area = 0.5 (Product of both the diagonals)

Now, in rhombus there is one triangle whose hypotenuse is 25cm.

And one side = 20 cm (Length of half diagonal)

So, by Pythagoras theorem.

$h^{2} = b^{2} +l^{2}$

$25^{2} =20^{2} +l^{2}$

$l^{2}=225$

l = 15 cm.

So, length of half of another diagonal is 15 cm.

Length of full diagonal = 2*15 = 30 cm.

Area = $\frac{30*40}{2}$

Area = 600 $cm^{2}$.

Hence, the area of rhombus is 600 $cm^{2}$.

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