Ram and Sham are making two different Kite s in the shape of Rhombuses.
Perimeter = 4 * a = 40 cm
=> the side of the Rhombus = 10 cm.
The internal angles and the diagonal sizes, and hence the areas of the two kites are different.
One of the diagonals of the kite is an integral multiple of 12 cm scale used.
The diagonals of the Kite of Ram are: X = 12 * k cm (a multiple of 12 cm, as a scale of 12 cm is used). The other diagonal is W cm, let us say.
Since in a Rhombus, 4 a² = X² + W²
4* 10² = 12² * k² + W^2
X, k are non zero positive integers and W is a positive real number.
if k = 1, then W = 16
So the diagonals are: 12 cm and 16 cm.
So the area of Ram's kite = 12 * 16/2= 96 cm²
Similarly for Sham's kite:
one of the diagonals of the kite is an integral multiple of 16 cm scale.
4 * a² = (16 k)² + N²
here k, N are positive and k is a positive integer.
4 * 100 = 256 * k² + N²
k = 1 and hence, N = 12 cm
So the diagonals are : 16 cm and 12 cm..
The area of the kite is : 16 * 12 / 2 = 96 cm²
The areas of blue and red paper are equal to 96 cm²