Question

The diagonals of a rhombus are 12cm and 16cm.find
i)the length of its one side
ii)its perimeter

Answer 1

i)One side= √6^2+√4^2
                 =√36+√16
                 =√52
ii)Perimeter = 4*side
                  =4√52

Answer 2

Let the side of the rhombus be x
The 2 diagonals of the rhombus divides it into 4 congruent right angled triangles
Let us consider 1 triangle among them
We get the side 'x' as the hypotenuse n other 2 sides are equal to halves of 2 diagonals respectively.
therefore, one of its side = 6cm
              another side = 8cm
From pythagoras theorem,
         8² + 6² = x²
        64 + 36 = x²
             100 = x²
Therefore, x = 10cm
length of one of the side of the rhombus is 10cm
Perimeter of the rhombus = 4 × 10 = 40cm