posted by dit
the length of the diagonals of a rhombus are in the ratio 3:4 if one side of the rhombus is 10 cm the length of both the diagonals of the rhombus
By the definition of a rhombus , all sides are equal, so if one side is 10, then all sides are equal to 10.
Also, the diagonals bisect each other at right angles creating 4 congruent right-angled triangles.
Looking at one of these triangles, we have sides
3x, 4x, and hypotenuse 10
9x^2 + 16x^2 = 100
25x^2 = 100
x^2 = 4
x = 2
Each triangle is 6 cm by 8 cm by 10 cm
According to my definitions, the diagonals would be 6x and 8x, or
12 cm and 16 cm.