Diagonal of a rhombus are in the ratio 3:4. If its perimeter is 40cm, find the length of the side and diagonals of rhombus

Answer 1

In a rhombus all 4 sides are equal, so each side = 10 cm

Since the diagonals bisect each other, the "half-diagonals" are also in the ration of 3 : 4
Let those half-diagonals be 3x and 4x

We have 4 congruent right-angled triangle, in each one:
(3x)^2 + (4x)^2 = 10^2
25x^2 = 100
x^2 = 4
x = 2
So the half-diagonals are 6 and 8 , making the diagonals equal to 12 and 16